Tag Archives: Quantum AI

Google at APS 2024

Today the 2024 March Meeting of the American Physical Society (APS) kicks off in Minneapolis, MN. A premier conference on topics ranging across physics and related fields, APS 2024 brings together researchers, students, and industry professionals to share their discoveries and build partnerships with the goal of realizing fundamental advances in physics-related sciences and technology.

This year, Google has a strong presence at APS with a booth hosted by the Google Quantum AI team, 50+ talks throughout the conference, and participation in conference organizing activities, special sessions and events. Attending APS 2024 in person? Come visit Google’s Quantum AI booth to learn more about the exciting work we’re doing to solve some of the field’s most interesting challenges.

You can learn more about the latest cutting edge work we are presenting at the conference along with our schedule of booth events below (Googlers listed in bold).

Organizing Committee

Session Chairs include: Aaron Szasz

Booth Activities

This schedule is subject to change. Please visit the Google Quantum AI booth for more information.

Presenter: Matt McEwen
Tue, Mar 5 | 11:00 AM CST

Presenter: Tanuj Khattar
Tue, Mar 5 | 2:30 PM CST

Presenter: Tanuj Khattar
Thu, Mar 7 | 11:00 AM CST

$5M XPRIZE / Google Quantum AI competition to accelerate quantum applications Q&A
Presenter: Ryan Babbush
Thu, Mar 7 | 11:00 AM CST



Certifying highly-entangled states from few single-qubit measurements
Presenter: Hsin-Yuan Huang
Author: Hsin-Yuan Huang
Session A45: New Frontiers in Machine Learning Quantum Physics

Toward high-fidelity analog quantum simulation with superconducting qubits
Presenter: Trond Andersen
Authors: Trond I Andersen, Xiao Mi, Amir H Karamlou, Nikita Astrakhantsev, Andrey Klots, Julia Berndtsson, Andre Petukhov, Dmitry Abanin, Lev B Ioffe, Yu Chen, Vadim Smelyanskiy, Pedram Roushan
Session A51: Applications on Noisy Quantum Hardware I

Measuring circuit errors in context for surface code circuits
Presenter: Dripto M Debroy
Authors: Dripto M Debroy, Jonathan A Gross, Élie Genois, Zhang Jiang
Session B50: Characterizing Noise with QCVV Techniques

Quantum computation of stopping power for inertial fusion target design I: Physics overview and the limits of classical algorithms
Presenter: Andrew D. Baczewski
Authors: Nicholas C. Rubin, Dominic W. Berry, Alina Kononov, Fionn D. Malone, Tanuj Khattar, Alec White, Joonho Lee, Hartmut Neven, Ryan Babbush, Andrew D. Baczewski
Session B51: Heterogeneous Design for Quantum Applications
Link to Paper

Quantum computation of stopping power for inertial fusion target design II: Physics overview and the limits of classical algorithms
Presenter: Nicholas C. Rubin
Authors: Nicholas C. Rubin, Dominic W. Berry, Alina Kononov, Fionn D. Malone, Tanuj Khattar, Alec White, Joonho Lee, Hartmut Neven, Ryan Babbush, Andrew D. Baczewski
Session B51: Heterogeneous Design for Quantum Applications
Link to Paper

Calibrating Superconducting Qubits: From NISQ to Fault Tolerance
Presenter: Sabrina S Hong
Author: Sabrina S Hong
Session B56: From NISQ to Fault Tolerance

Measurement and feedforward induced entanglement negativity transition
Presenter: Ramis Movassagh
Authors: Alireza Seif, Yu-Xin Wang, Ramis Movassagh, Aashish A. Clerk
Session B31: Measurement Induced Criticality in Many-Body Systems
Link to Paper

Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments
Presenter: Salvatore Mandra
Authors: Kostyantyn Kechedzhi, Sergei V Isakov, Salvatore Mandra, Benjamin Villalonga, X. Mi, Sergio Boixo, Vadim Smelyanskiy
Session B52: Quantum Algorithms and Complexity
Link to Paper

Accurate thermodynamic tables for solids using Machine Learning Interaction Potentials and Covariance of Atomic Positions
Presenter: Mgcini K Phuthi
Authors: Mgcini K Phuthi, Yang Huang, Michael Widom, Ekin D Cubuk, Venkat Viswanathan
Session D60: Machine Learning of Molecules and Materials: Chemical Space and Dynamics


IN-Situ Pulse Envelope Characterization Technique (INSPECT)
Presenter: Zhang Jiang
Authors: Zhang Jiang, Jonathan A Gross, Élie Genois
Session F50: Advanced Randomized Benchmarking and Gate Calibration

Characterizing two-qubit gates with dynamical decoupling
Presenter: Jonathan A Gross
Authors: Jonathan A Gross, Zhang Jiang, Élie Genois, Dripto M Debroy, Ze-Pei Cian*, Wojciech Mruczkiewicz
Session F50: Advanced Randomized Benchmarking and Gate Calibration

Statistical physics of regression with quadratic models
Presenter: Blake Bordelon
Authors: Blake Bordelon, Cengiz Pehlevan, Yasaman Bahri
Session EE01: V: Statistical and Nonlinear Physics II

Improved state preparation for first-quantized simulation of electronic structure
Presenter: William J Huggins
Authors: William J Huggins, Oskar Leimkuhler, Torin F Stetina, Birgitta Whaley
Session G51: Hamiltonian Simulation

Controlling large superconducting quantum processors
Presenter: Paul V. Klimov
Authors: Paul V. Klimov, Andreas Bengtsson, Chris Quintana, Alexandre Bourassa, Sabrina Hong, Andrew Dunsworth, Kevin J. Satzinger, William P. Livingston, Volodymyr Sivak, Murphy Y. Niu, Trond I. Andersen, Yaxing Zhang, Desmond Chik, Zijun Chen, Charles Neill, Catherine Erickson, Alejandro Grajales Dau, Anthony Megrant, Pedram Roushan, Alexander N. Korotkov, Julian Kelly, Vadim Smelyanskiy, Yu Chen, Hartmut Neven
Session G30: Commercial Applications of Quantum Computing)
Link to Paper

Gaussian boson sampling: Determining quantum advantage
Presenter: Peter D Drummond
Authors: Peter D Drummond, Alex Dellios, Ned Goodman, Margaret D Reid, Ben Villalonga
Session G50: Quantum Characterization, Verification, and Validation II

Attention to complexity III: learning the complexity of random quantum circuit states
Presenter: Hyejin Kim
Authors: Hyejin Kim, Yiqing Zhou, Yichen Xu, Chao Wan, Jin Zhou, Yuri D Lensky, Jesse Hoke, Pedram Roushan, Kilian Q Weinberger, Eun-Ah Kim
Session G50: Quantum Characterization, Verification, and Validation II

Balanced coupling in superconducting circuits
Presenter: Daniel T Sank
Authors: Daniel T Sank, Sergei V Isakov, Mostafa Khezri, Juan Atalaya
Session K48: Strongly Driven Superconducting Systems

Resource estimation of Fault Tolerant algorithms using Qᴜᴀʟᴛʀᴀɴ
Presenter: Tanuj Khattar
Author: Tanuj Khattar
Session K49: Algorithms and Implementations on Near-Term Quantum Computers


Discovering novel quantum dynamics with superconducting qubits
Presenter: Pedram Roushan
Author: Pedram Roushan
Session M24: Analog Quantum Simulations Across Platforms

Deciphering Tumor Heterogeneity in Triple-Negative Breast Cancer: The Crucial Role of Dynamic Cell-Cell and Cell-Matrix Interactions
Presenter: Susan Leggett
Authors: Susan Leggett, Ian Wong, Celeste Nelson, Molly Brennan, Mohak Patel, Christian Franck, Sophia Martinez, Joe Tien, Lena Gamboa, Thomas Valentin, Amanda Khoo, Evelyn K Williams
Session M27: Mechanics of Cells and Tissues II

Toward implementation of protected charge-parity qubits
Presenter: Abigail Shearrow
Authors: Abigail Shearrow, Matthew Snyder, Bradley G Cole, Kenneth R Dodge, Yebin Liu, Andrey Klots, Lev B Ioffe, Britton L Plourde, Robert McDermott
Session N48: Unconventional Superconducting Qubits

Electronic capacitance in tunnel junctions for protected charge-parity qubits
Presenter: Bradley G Cole
Authors: Bradley G Cole, Kenneth R Dodge, Yebin Liu, Abigail Shearrow, Matthew Snyder, Andrey Klots, Lev B Ioffe, Robert McDermott, B.L.T. Plourde
Session N48: Unconventional Superconducting Qubits

Overcoming leakage in quantum error correction
Presenter: Kevin C. Miao
Authors: Kevin C. Miao, Matt McEwen, Juan Atalaya, Dvir Kafri, Leonid P. Pryadko, Andreas Bengtsson, Alex Opremcak, Kevin J. Satzinger, Zijun Chen, Paul V. Klimov, Chris Quintana, Rajeev Acharya, Kyle Anderson, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Joseph C. Bardin, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Juan Campero, Ben Chiaro, Roberto Collins, Paul Conner, Alexander L. Crook, Ben Curtin, Dripto M. Debroy, Sean Demura, Andrew Dunsworth, Catherine Erickson, Reza Fatemi, Vinicius S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, Gonzalo Garcia, William Giang, Craig Gidney, Marissa Giustina, Raja Gosula, Alejandro Grajales Dau, Jonathan A. Gross, Michael C. Hamilton, Sean D. Harrington, Paula Heu, Jeremy Hilton, Markus R. Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Julian Kelly, Seon Kim, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, Lily Laws, Kenny Lee, Brian J. Lester, Alexander T. Lill, Wayne Liu, Aditya Locharla, Erik Lucero, Steven Martin, Anthony Megrant, Xiao Mi, Shirin Montazeri, Alexis Morvan, Ofer Naaman, Matthew Neeley, Charles Neill, Ani Nersisyan, Michael Newman, Jiun How Ng, Anthony Nguyen, Murray Nguyen, Rebecca Potter, Charles Rocque, Pedram Roushan, Kannan Sankaragomathi, Christopher Schuster, Michael J. Shearn, Aaron Shorter, Noah Shutty, Vladimir Shvarts, Jindra Skruzny, W. Clarke Smith, George Sterling, Marco Szalay, Douglas Thor, Alfredo Torres, Theodore White, Bryan W. K. Woo, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Grayson Young, Adam Zalcman, Ningfeng Zhu, Nicholas Zobrist, Hartmut Neven, Vadim Smelyanskiy, Andre Petukhov, Alexander N. Korotkov, Daniel Sank, Yu Chen
Session N51: Quantum Error Correction Code Performance and Implementation I
Link to Paper

Modeling the performance of the surface code with non-uniform error distribution: Part 1
Presenter: Yuri D Lensky
Authors: Yuri D Lensky, Volodymyr Sivak, Kostyantyn Kechedzhi, Igor Aleiner
Session N51: Quantum Error Correction Code Performance and Implementation I

Modeling the performance of the surface code with non-uniform error distribution: Part 2
Presenter: Volodymyr Sivak
Authors: Volodymyr Sivak, Michael Newman, Cody Jones, Henry Schurkus, Dvir Kafri, Yuri D Lensky, Paul Klimov, Kostyantyn Kechedzhi, Vadim Smelyanskiy
Session N51: Quantum Error Correction Code Performance and Implementation I

Highly optimized tensor network contractions for the simulation of classically challenging quantum computations
Presenter: Benjamin Villalonga
Author: Benjamin Villalonga
Session Q51: Co-evolution of Quantum Classical Algorithms

Teaching modern quantum computing concepts using hands-on open-source software at all levels
Presenter: Abraham Asfaw
Author: Abraham Asfaw
Session Q61: Teaching Quantum Information at All Levels II


New circuits and an open source decoder for the color code
Presenter: Craig Gidney
Authors: Craig Gidney, Cody Jones
Session S51: Quantum Error Correction Code Performance and Implementation II
Link to Paper

Performing Hartree-Fock many-body physics calculations with large language models
Presenter: Eun-Ah Kim
Authors: Eun-Ah Kim, Haining Pan, Nayantara Mudur, William Taranto, Subhashini Venugopalan, Yasaman Bahri, Michael P Brenner
Session S18: Data Science, AI and Machine Learning in Physics I

New methods for reducing resource overhead in the surface code
Presenter: Michael Newman
Authors: Craig M Gidney, Michael Newman, Peter Brooks, Cody Jones
Session S51: Quantum Error Correction Code Performance and Implementation II
Link to Paper

Challenges and opportunities for applying quantum computers to drug design
Presenter: Raffaele Santagati
Authors: Raffaele Santagati, Alan Aspuru-Guzik, Ryan Babbush, Matthias Degroote, Leticia Gonzalez, Elica Kyoseva, Nikolaj Moll, Markus Oppel, Robert M. Parrish, Nicholas C. Rubin, Michael Streif, Christofer S. Tautermann, Horst Weiss, Nathan Wiebe, Clemens Utschig-Utschig
Session S49: Advances in Quantum Algorithms for Near-Term Applications
Link to Paper

Dispatches from Google's hunt for super-quadratic quantum advantage in new applications
Presenter: Ryan Babbush
Author: Ryan Babbush
Session T45: Recent Advances in Quantum Algorithms

Qubit as a reflectometer
Presenter: Yaxing Zhang
Authors: Yaxing Zhang, Benjamin Chiaro
Session T48: Superconducting Fabrication, Packaging, & Validation

Random-matrix theory of measurement-induced phase transitions in nonlocal Floquet quantum circuits
Presenter: Aleksei Khindanov
Authors: Aleksei Khindanov, Lara Faoro, Lev Ioffe, Igor Aleiner
Session W14: Measurement-Induced Phase Transitions

Continuum limit of finite density many-body ground states with MERA
Presenter: Subhayan Sahu
Authors: Subhayan Sahu, Guifré Vidal
Session W58: Extreme-Scale Computational Science Discovery in Fluid Dynamics and Related Disciplines II

Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
Presenter: Eliott Rosenberg
Authors: Eliott Rosenberg, Trond Andersen, Rhine Samajdar, Andre Petukhov, Jesse Hoke*, Dmitry Abanin, Andreas Bengtsson, Ilya Drozdov, Catherine Erickson, Paul Klimov, Xiao Mi, Alexis Morvan, Matthew Neeley, Charles Neill, Rajeev Acharya, Richard Allen, Kyle Anderson, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Joseph Bardin, A. Bilmes, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, Bob B. Buckley, David Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Juan Campero, Hung-Shen Chang, Zijun Chen, Benjamin Chiaro, Desmond Chik, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander Crook, Ben Curtin, Dripto Debroy, Alexander Del Toro Barba, Sean Demura, Agustin Di Paolo, Andrew Dunsworth, Clint Earle, E. Farhi, Reza Fatemi, Vinicius Ferreira, Leslie Flores, Ebrahim Forati, Austin Fowler, Brooks Foxen, Gonzalo Garcia, Élie Genois, William Giang, Craig Gidney, Dar Gilboa, Marissa Giustina, Raja Gosula, Alejandro Grajales Dau, Jonathan Gross, Steve Habegger, Michael Hamilton, Monica Hansen, Matthew Harrigan, Sean Harrington, Paula Heu, Gordon Hill, Markus Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, William Huggins, Lev Ioffe, Sergei Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Pavol Juhas, D. Kafri, Tanuj Khattar, Mostafa Khezri, Mária Kieferová, Seon Kim, Alexei Kitaev, Andrey Klots, Alexander Korotkov, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, Kim Ming Lau, Lily Laws, Joonho Lee, Kenneth Lee, Yuri Lensky, Brian Lester, Alexander Lill, Wayne Liu, William P. Livingston, A. Locharla, Salvatore Mandrà, Orion Martin, Steven Martin, Jarrod McClean, Matthew McEwen, Seneca Meeks, Kevin Miao, Amanda Mieszala, Shirin Montazeri, Ramis Movassagh, Wojciech Mruczkiewicz, Ani Nersisyan, Michael Newman, Jiun How Ng, Anthony Nguyen, Murray Nguyen, M. Niu, Thomas O'Brien, Seun Omonije, Alex Opremcak, Rebecca Potter, Leonid Pryadko, Chris Quintana, David Rhodes, Charles Rocque, N. Rubin, Negar Saei, Daniel Sank, Kannan Sankaragomathi, Kevin Satzinger, Henry Schurkus, Christopher Schuster, Michael Shearn, Aaron Shorter, Noah Shutty, Vladimir Shvarts, Volodymyr Sivak, Jindra Skruzny, Clarke Smith, Rolando Somma, George Sterling, Doug Strain, Marco Szalay, Douglas Thor, Alfredo Torres, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Theodore White, Bryan Woo, Cheng Xing, Jamie Yao, Ping Yeh, Juhwan Yoo, Grayson Young, Adam Zalcman, Yaxing Zhang, Ningfeng Zhu, Nicholas Zobrist, Hartmut Neven, Ryan Babbush, Dave Bacon, Sergio Boixo, Jeremy Hilton, Erik Lucero, Anthony Megrant, Julian Kelly, Yu Chen, Vadim Smelyanskiy, Vedika Khemani, Sarang Gopalakrishnan, Tomaž Prosen, Pedram Roushan
Session W50: Quantum Simulation of Many-Body Physics
Link to Paper

The fast multipole method on a quantum computer
Presenter: Kianna Wan
Authors: Kianna Wan, Dominic W Berry, Ryan Babbush
Session W50: Quantum Simulation of Many-Body Physics


The quantum computing industry and protecting national security: what tools will work?
Presenter: Kate Weber
Author: Kate Weber
Session Y43: Industry, Innovation, and National Security: Finding the Right Balance

Novel charging effects in the fluxonium qubit
Presenter: Agustin Di Paolo
Authors: Agustin Di Paolo, Kyle Serniak, Andrew J Kerman, William D Oliver
Session Y46: Fluxonium-Based Superconducting Quibits

Microwave Engineering of Parametric Interactions in Superconducting Circuits
Presenter: Ofer Naaman
Author: Ofer Naaman
Session Z46: Broadband Parametric Amplifiers and Circulators

Linear spin wave theory of large magnetic unit cells using the Kernel Polynomial Method
Presenter: Harry Lane
Authors: Harry Lane, Hao Zhang, David A Dahlbom, Sam Quinn, Rolando D Somma, Martin P Mourigal, Cristian D Batista, Kipton Barros
Session Z62: Cooperative Phenomena, Theory

*Work done while at Google

Source: Google AI Blog

A new quantum algorithm for classical mechanics with an exponential speedup

Quantum computers promise to solve some problems exponentially faster than classical computers, but there are only a handful of examples with such a dramatic speedup, such as Shor’s factoring algorithm and quantum simulation. Of those few examples, the majority of them involve simulating physical systems that are inherently quantum mechanical — a natural application for quantum computers. But what about simulating systems that are not inherently quantum? Can quantum computers offer an exponential advantage for this?

In “Exponential quantum speedup in simulating coupled classical oscillators”, published in Physical Review X (PRX) and presented at the Symposium on Foundations of Computer Science (FOCS 2023), we report on the discovery of a new quantum algorithm that offers an exponential advantage for simulating coupled classical harmonic oscillators. These are some of the most fundamental, ubiquitous systems in nature and can describe the physics of countless natural systems, from electrical circuits to molecular vibrations to the mechanics of bridges. In collaboration with Dominic Berry of Macquarie University and Nathan Wiebe of the University of Toronto, we found a mapping that can transform any system involving coupled oscillators into a problem describing the time evolution of a quantum system. Given certain constraints, this problem can be solved with a quantum computer exponentially faster than it can with a classical computer. Further, we use this mapping to prove that any problem efficiently solvable by a quantum algorithm can be recast as a problem involving a network of coupled oscillators, albeit exponentially many of them. In addition to unlocking previously unknown applications of quantum computers, this result provides a new method of designing new quantum algorithms by reasoning purely about classical systems.

Simulating coupled oscillators

The systems we consider consist of classical harmonic oscillators. An example of a single harmonic oscillator is a mass (such as a ball) attached to a spring. If you displace the mass from its rest position, then the spring will induce a restoring force, pushing or pulling the mass in the opposite direction. This restoring force causes the mass to oscillate back and forth.

A simple example of a harmonic oscillator is a mass connected to a wall by a spring. [Image Source: Wikimedia]

Now consider coupled harmonic oscillators, where multiple masses are attached to one another through springs. Displace one mass, and it will induce a wave of oscillations to pulse through the system. As one might expect, simulating the oscillations of a large number of masses on a classical computer gets increasingly difficult.

An example system of masses connected by springs that can be simulated with the quantum algorithm.

To enable the simulation of a large number of coupled harmonic oscillators, we came up with a mapping that encodes the positions and velocities of all masses and springs into the quantum wavefunction of a system of qubits. Since the number of parameters describing the wavefunction of a system of qubits grows exponentially with the number of qubits, we can encode the information of N balls into a quantum mechanical system of only about log(N) qubits. As long as there is a compact description of the system (i.e., the properties of the masses and the springs), we can evolve the wavefunction to learn coordinates of the balls and springs at a later time with far fewer resources than if we had used a naïve classical approach to simulate the balls and springs.

We showed that a certain class of coupled-classical oscillator systems can be efficiently simulated on a quantum computer. But this alone does not rule out the possibility that there exists some as-yet-unknown clever classical algorithm that is similarly efficient in its use of resources. To show that our quantum algorithm achieves an exponential speedup over any possible classical algorithm, we provide two additional pieces of evidence.

The glued-trees problem and the quantum oracle

For the first piece of evidence, we use our mapping to show that the quantum algorithm can efficiently solve a famous problem about graphs known to be difficult to solve classically, called the glued-trees problem. The problem takes two branching trees — a graph whose nodes each branch to two more nodes, resembling the branching paths of a tree — and glues their branches together through a random set of edges, as shown in the figure below.

A visual representation of the glued trees problem. Here we start at the node labeled ENTRANCE and are allowed to locally explore the graph, which is obtained by randomly gluing together two binary trees. The goal is to find the node labeled EXIT.

The goal of the glued-trees problem is to find the exit node — the “root” of the second tree — as efficiently as possible. But the exact configuration of the nodes and edges of the glued trees are initially hidden from us. To learn about the system, we must query an oracle, which can answer specific questions about the setup. This oracle allows us to explore the trees, but only locally. Decades ago, it was shown that the number of queries required to find the exit node on a classical computer is proportional to a polynomial factor of N, the total number of nodes.

But recasting this as a problem with balls and springs, we can imagine each node as a ball and each connection between two nodes as a spring. Pluck the entrance node (the root of the first tree), and the oscillations will pulse through the trees. It only takes a time that scales with the depth of the tree — which is exponentially smaller than N — to reach the exit node. So, by mapping the glued-trees ball-and-spring system to a quantum system and evolving it for that time, we can detect the vibrations of the exit node and determine it exponentially faster than we could using a classical computer.


The second and strongest piece of evidence that our algorithm is exponentially more efficient than any possible classical algorithm is revealed by examination of the set of problems a quantum computer can solve efficiently (i.e., solvable in polynomial time), referred to as bounded-error quantum polynomial time or BQP. The hardest problems in BQP are called “BQP-complete”.

While it is generally accepted that there exist some problems that a quantum algorithm can solve efficiently and a classical algorithm cannot, this has not yet been proven. So, the best evidence we can provide is that our problem is BQP-complete, that is, it is among the hardest problems in BQP. If someone were to find an efficient classical algorithm for solving our problem, then every problem solved by a quantum computer efficiently would be classically solvable! Not even the factoring problem (finding the prime factors of a given large number), which forms the basis of modern encryption and was famously solved by Shor’s algorithm, is expected to be BQP-complete.

A diagram showing the believed relationships of the classes BPP and BQP, which are the set of problems that can be efficiently solved on a classical computer and quantum computer, respectively. BQP-complete problems are the hardest problems in BQP.

To show that our problem of simulating balls and springs is indeed BQP-complete, we start with a standard BQP-complete problem of simulating universal quantum circuits, and show that every quantum circuit can be expressed as a system of many balls coupled with springs. Therefore, our problem is also BQP-complete.

Implications and future work

This effort also sheds light on work from 2002, when theoretical computer scientist Lov K. Grover and his colleague, Anirvan M. Sengupta, used an analogy to coupled pendulums to illustrate how Grover’s famous quantum search algorithm could find the correct element in an unsorted database quadratically faster than could be done classically. With the proper setup and initial conditions, it would be possible to tell whether one of N pendulums was different from the others — the analogue of finding the correct element in a database — after the system had evolved for time that was only ~√(N). While this hints at a connection between certain classical oscillating systems and quantum algorithms, it falls short of explaining why Grover’s quantum algorithm achieves a quantum advantage.

Our results make that connection precise. We showed that the dynamics of any classical system of harmonic oscillators can indeed be equivalently understood as the dynamics of a corresponding quantum system of exponentially smaller size. In this way we can simulate Grover and Sengupta’s system of pendulums on a quantum computer of log(N) qubits, and find a different quantum algorithm that can find the correct element in time ~√(N). The analogy we discovered between classical and quantum systems can be used to construct other quantum algorithms offering exponential speedups, where the reason for the speedups is now more evident from the way that classical waves propagate.

Our work also reveals that every quantum algorithm can be equivalently understood as the propagation of a classical wave in a system of coupled oscillators. This would imply that, for example, we can in principle build a classical system that solves the factoring problem after it has evolved for time that is exponentially smaller than the runtime of any known classical algorithm that solves factoring. This may look like an efficient classical algorithm for factoring, but the catch is that the number of oscillators is exponentially large, making it an impractical way to solve factoring.

Coupled harmonic oscillators are ubiquitous in nature, describing a broad range of systems from electrical circuits to chains of molecules to structures such as bridges. While our work here focuses on the fundamental complexity of this broad class of problems, we expect that it will guide us in searching for real-world examples of harmonic oscillator problems in which a quantum computer could offer an exponential advantage.


We would like to thank our Quantum Computing Science Communicator, Katie McCormick, for helping to write this blog post.

Source: Google AI Blog

Overcoming leakage on error-corrected quantum processors

The qubits that make up Google quantum devices are delicate and noisy, so it’s necessary to incorporate error correction procedures that identify and account for qubit errors on the way to building a useful quantum computer. Two of the most prevalent error mechanisms are bit-flip errors (where the energy state of the qubit changes) and phase-flip errors (where the phase of the encoded quantum information changes). Quantum error correction (QEC) promises to address and mitigate these two prominent errors. However, there is an assortment of other error mechanisms that challenges the effectiveness of QEC.

While we want qubits to behave as ideal two-level systems with no loss mechanisms, this is not the case in reality. We use the lowest two energy levels of our qubit (which form the computational basis) to carry out computations. These two levels correspond to the absence (computational ground state) or presence (computational excited state) of an excitation in the qubit, and are labeled |0⟩ (“ket zero”) and |1⟩ (“ket one”), respectively. However, our qubits also host many higher levels called leakage states, which can become occupied. Following the convention of labeling the level by indicating how many excitations are in the qubit, we specify them as |2⟩, |3⟩, |4⟩, and so on.

In “Overcoming leakage in quantum error correction”, published in Nature Physics, we identify when and how our qubits leak energy to higher states, and show that the leaked states can corrupt nearby qubits through our two-qubit gates. We then identify and implement a strategy that can remove leakage and convert it to an error that QEC can efficiently fix. Finally, we show that these operations lead to notably improved performance and stability of the QEC process. This last result is particularly critical, since additional operations take time, usually leading to more errors.

Working with imperfect qubits

Our quantum processors are built from superconducting qubits called transmons. Unlike an ideal qubit, which only has two computational levels — a computational ground state and a computational excited state — transmon qubits have many additional states with higher energy than the computational excited state. These higher leakage states are useful for particular operations that generate entanglement, a necessary resource in quantum algorithms, and also keep transmons from becoming too non-linear and difficult to operate. However, the transmon can also be inadvertently excited into these leakage states through a variety of processes, including imperfections in the control pulses we apply to perform operations or from the small amount of stray heat leftover in our cryogenic refrigerator. These processes are collectively referred to as leakage, which describes the transition of the qubit from computational states to leakage states.

Consider a particular two-qubit operation that is used extensively in our QEC experiments: the CZ gate. This gate operates on two qubits, and when both qubits are in their |1⟩ level, an interaction causes the two individual excitations to briefly “bunch” together in one of the qubits to form |2⟩, while the other qubit becomes |0⟩, before returning to the original configuration where each qubit is in |1⟩. This bunching underlies the entangling power of the CZ gate. However, with a small probability, the gate can encounter an error and the excitations do not return to their original configuration, causing the operation to leave a qubit in |2⟩, a leakage state. When we execute hundreds or more of these CZ gates, this small leakage error probability accumulates.

Transmon qubits support many leakage states (|2⟩, |3⟩, |4⟩, …) beyond the computational basis (|0⟩ and |1⟩). While we typically only use the computational basis to represent quantum information, sometimes the qubit enters these leakage states, and disrupts the normal operation of our qubits.

A single leakage event is especially damaging to normal qubit operation because it induces many individual errors. When one qubit starts in a leaked state, the CZ gate no longer correctly entangles the qubits, preventing the algorithm from executing correctly. Not only that, but CZ gates applied to one qubit in leaked states can cause the other qubit to leak as well, spreading leakage through the device. Our work includes extensive characterization of how leakage is caused and how it interacts with the various operations we use in our quantum processor.

Once the qubit enters a leakage state, it can remain in that state for many operations before relaxing back to the computational states. This means that a single leakage event interferes with many operations on that qubit, creating operational errors that are bunched together in time (time-correlated errors). The ability for leakage to spread between the different qubits in our device through the CZ gates means we also concurrently see bunches of errors on neighboring qubits (space-correlated errors). The fact that leakage induces patterns of space- and time-correlated errors makes it especially hard to diagnose and correct from the perspective of QEC algorithms.

The effect of leakage in QEC

We aim to mitigate qubit errors by implementing surface code QEC, a set of operations applied to a collection of imperfect physical qubits to form a logical qubit, which has properties much closer to an ideal qubit. In a nutshell, we use a set of qubits called data qubits to hold the quantum information, while another set of measure qubits check up on the data qubits, reporting on whether they have suffered any errors, without destroying the delicate quantum state of the data qubits. One of the key underlying assumptions of QEC is that errors occur independently for each operation, but leakage can persist over many operations and cause a correlated pattern of multiple errors. The performance of our QEC strategies is significantly limited when leakage causes this assumption to be violated.

Once leakage manifests in our surface code transmon grid, it persists for a long time relative to a single surface code QEC cycle. To make matters worse, leakage on one qubit can cause its neighbors to leak as well.

Our previous work has shown that we can remove leakage from measure qubits using an operation called multi-level reset (MLR). This is possible because once we perform a measurement on measure qubits, they no longer hold any important quantum information. At this point, we can interact the qubit with a very lossy frequency band, causing whichever state the qubit was in (including leakage states) to decay to the computational ground state |0⟩. If we picture a Jenga tower representing the excitations in the qubit, we tumble the entire stack over. Removing just one brick, however, is much more challenging. Likewise, MLR doesn’t work with data qubits because they always hold important quantum information, so we need a new leakage removal approach that minimally disturbs the computational basis states.

Gently removing leakage

We introduce a new quantum operation called data qubit leakage removal (DQLR), which targets leakage states in a data qubit and converts them into computational states in the data qubit and a neighboring measure qubit. DQLR consists of a two-qubit gate (dubbed Leakage iSWAP — an iSWAP operation with leakage states) inspired by and similar to our CZ gate, followed by a rapid reset of the measure qubit to further remove errors. The Leakage iSWAP gate is very efficient and greatly benefits from our extensive characterization and calibration of CZ gates within the surface code experiment.

Recall that a CZ gate takes two single excitations on two different qubits and briefly brings them to one qubit, before returning them to their respective qubits. A Leakage iSWAP gate operates similarly, but almost in reverse, so that it takes a single qubit with two excitations (otherwise known as |2⟩) and splits them into |1⟩ on two qubits. The Leakage iSWAP gate (and for that matter, the CZ gate) is particularly effective because it does not operate on the qubits if there are fewer than two excitations present. We are precisely removing the |2⟩ Jenga brick without toppling the entire tower.

By carefully measuring the population of leakage states on our transmon grid, we find that DQLR can reduce average leakage state populations over all qubits to about 0.1%, compared to nearly 1% without it. Importantly, we no longer observe a gradual rise in the amount of leakage on the data qubits, which was always present to some extent prior to using DQLR.

This outcome, however, is only half of the puzzle. As mentioned earlier, an operation such as MLR could be used to effectively remove leakage on the data qubits, but it would also completely erase the stored quantum state. We also need to demonstrate that DQLR is compatible with the preservation of a logical quantum state.

The second half of the puzzle comes from executing the QEC experiment with this operation interleaved at the end of each QEC cycle, and observing the logical performance. Here, we use a metric called detection probability to gauge how well we are executing QEC. In the presence of leakage, time- and space-correlated errors will cause a gradual rise in detection probabilities as more and more qubits enter and stay in leakage states. This is most evident when we perform no reset at all, which rapidly leads to a transmon grid plagued by leakage, and it becomes inoperable for the purposes of QEC.

The prior state-of-the-art in our QEC experiments was to use MLR on the measure qubits to remove leakage. While this kept leakage population on the measure qubits (green circles) sufficiently low, data qubit leakage population (green squares) would grow and saturate to a few percent. With DQLR, leakage population on both the measure (blue circles) and data qubits (blue squares) remain acceptably low and stable.

With MLR, the large reduction in leakage population on the measure qubits drastically decreases detection probabilities and mitigates a considerable degree of the gradual rise. This reduction in detection probability happens even though we spend more time dedicated to the MLR gate, when other errors can potentially occur. Put another way, the correlated errors that leakage causes on the grid can be much more damaging than the uncorrelated errors from the qubits waiting idle, and it is well worth it for us to trade the former for the latter.

When only using MLR, we observed a small but persistent residual rise in detection probabilities. We ascribed this residual increase in detection probability to leakage accumulating on the data qubits, and found that it disappeared when we implemented DQLR. And again, the observation that the detection probabilities end up lower compared to only using MLR indicates that our added operation has removed a damaging error mechanism while minimally introducing uncorrelated errors.

Leakage manifests during surface code operation as increased errors (shown as error detection probabilities) over the number of cycles. With DQLR, we no longer see a notable rise in detection probability over more surface code cycles.

Prospects for QEC scale-up

Given these promising results, we are eager to implement DQLR in future QEC experiments, where we expect error mechanisms outside of leakage to be greatly improved, and sensitivity to leakage to be enhanced as we work with larger and larger transmon grids. In particular, our simulations indicate that scale-up of our surface code will almost certainly require a large reduction in leakage generation rates, or an active leakage removal technique over all qubits, such as DQLR.

Having laid the groundwork by understanding where leakage is generated, capturing the dynamics of leakage after it presents itself in a transmon grid, and showing that we have an effective mitigation strategy in DQLR, we believe that leakage and its associated errors no longer pose an existential threat to the prospects of executing a surface code QEC protocol on a large grid of transmon qubits. With one fewer challenge standing in the way of demonstrating working QEC, the pathway to a useful quantum computer has never been more promising.


This work would not have been possible without the contributions of the entire Google Quantum AI Team.

Source: Google AI Blog

Measurement-induced entanglement phase transitions in a quantum circuit

Quantum mechanics allows many phenomena that are classically impossible: a quantum particle can exist in a superposition of two states simultaneously or be entangled with another particle, such that anything you do to one seems to instantaneously also affect the other, regardless of the space between them. But perhaps no aspect of quantum theory is as striking as the act of measurement. In classical mechanics, a measurement need not affect the system being studied. But a measurement on a quantum system can profoundly influence its behavior. For example, when a quantum bit of information, called a qubit, that is in a superposition of both “0” and “1” is measured, its state will suddenly collapse to one of the two classically allowed states: it will be either “0” or “1,” but not both. This transition from the quantum to classical worlds seems to be facilitated by the act of measurement. How exactly it occurs is one of the fundamental unanswered questions in physics.

In a large system comprising many qubits, the effect of measurements can cause new phases of quantum information to emerge. Similar to how changing parameters such as temperature and pressure can cause a phase transition in water from liquid to solid, tuning the strength of measurements can induce a phase transition in the entanglement of qubits.

Today in “Measurement-induced entanglement and teleportation on a noisy quantum processor”, published in Nature, we describe experimental observations of measurement-induced effects in a system of 70 qubits on our Sycamore quantum processor. This is, by far, the largest system in which such a phase transition has been observed. Additionally, we detected "quantum teleportation" — when a quantum state is transferred from one set of qubits to another, detectable even if the details of that state are unknown — which emerged from measurements of a random circuit. We achieved this breakthrough by implementing a few clever “tricks” to more readily see the signatures of measurement-induced effects in the system.

Background: Measurement-induced entanglement

Consider a system of qubits that start out independent and unentangled with one another. If they interact with one another , they will become entangled. You can imagine this as a web, where the strands represent the entanglement between qubits. As time progresses, this web grows larger and more intricate, connecting increasingly disparate points together.

A full measurement of the system completely destroys this web, since every entangled superposition of qubits collapses when it’s measured. But what happens when we make a measurement on only a few of the qubits? Or if we wait a long time between measurements? During the intervening time, entanglement continues to grow. The web’s strands may not extend as vastly as before, but there are still patterns in the web.

There is a balancing point between the strength of interactions and measurements, which compete to affect the intricacy of the web. When interactions are strong and measurements are weak, entanglement remains robust and the web’s strands extend farther, but when measurements begin to dominate, the entanglement web is destroyed. We call the crossover between these two extremes the measurement-induced phase transition.

In our quantum processor, we observe this measurement-induced phase transition by varying the relative strengths between interactions and measurement. We induce interactions by performing entangling operations on pairs of qubits. But to actually see this web of entanglement in an experiment is notoriously challenging. First, we can never actually look at the strands connecting the qubits — we can only infer their existence by seeing statistical correlations between the measurement outcomes of the qubits. So, we need to repeat the same experiment many times to infer the pattern of the web. But there’s another complication: the web pattern is different for each possible measurement outcome. Simply averaging all of the experiments together without regard for their measurement outcomes would wash out the webs’ patterns. To address this, some previous experiments used “post-selection,” where only data with a particular measurement outcome is used and the rest is thrown away. This, however, causes an exponentially decaying bottleneck in the amount of “usable” data you can acquire. In addition, there are also practical challenges related to the difficulty of mid-circuit measurements with superconducting qubits and the presence of noise in the system.

How we did it

To address these challenges, we introduced three novel tricks to the experiment that enabled us to observe measurement-induced dynamics in a system of up to 70 qubits.

Trick 1: Space and time are interchangeable

As counterintuitive as it may seem, interchanging the roles of space and time dramatically reduces the technical challenges of the experiment. Before this “space-time duality” transformation, we would have had to interleave measurements with other entangling operations, frequently checking the state of selected qubits. Instead, after the transformation, we can postpone all measurements until after all other operations, which greatly simplifies the experiment. As implemented here, this transformation turns the original 1-spatial-dimensional circuit we were interested in studying into a 2-dimensional one. Additionally, since all measurements are now at the end of the circuit, the relative strength of measurements and entangling interactions is tuned by varying the number of entangling operations performed in the circuit.

Exchanging space and time. To avoid the complication of interleaving measurements into our experiment (shown as gauges in the left panel), we utilize a space-time duality mapping to exchange the roles of space and time. This mapping transforms the 1D circuit (left) into a 2D circuit (right), where the circuit depth (T) now tunes the effective measurement rate.

Trick 2: Overcoming the post-selection bottleneck

Since each combination of measurement outcomes on all of the qubits results in a unique web pattern of entanglement, researchers often use post-selection to examine the details of a particular web. However, because this method is very inefficient, we developed a new “decoding” protocol that compares each instance of the real “web” of entanglement to the same instance in a classical simulation. This avoids post-selection and is sensitive to features that are common to all of the webs. This common feature manifests itself into a combined classical–quantum “order parameter”, akin to the cross-entropy benchmark used in the random circuit sampling used in our beyond-classical demonstration.

This order parameter is calculated by selecting one of the qubits in the system as the “probe” qubit, measuring it, and then using the measurement record of the nearby qubits to classically “decode” what the state of the probe qubit should be. By cross-correlating the measured state of the probe with this “decoded” prediction, we can obtain the entanglement between the probe qubit and the rest of the (unmeasured) qubits. This serves as an order parameter, which is a proxy for determining the entanglement characteristics of the entire web.

In the decoding procedure we choose a “probe” qubit (pink) and classically compute its expected value, conditional on the measurement record of the surrounding qubits (yellow). The order parameter is then calculated by the cross correlation between the measured probe bit and the classically computed value.

Trick 3: Using noise to our advantage

A key feature of the so-called “disentangling phase” — where measurements dominate and entanglement is less widespread — is its insensitivity to noise. We can therefore look at how the probe qubit is affected by noise in the system and use that to differentiate between the two phases. In the disentangling phase, the probe will be sensitive only to local noise that occurs within a particular area near the probe. On the other hand, in the entangling phase, any noise in the system can affect the probe qubit. In this way, we are turning something that is normally seen as a nuisance in experiments into a unique probe of the system.

What we saw

We first studied how the order parameter was affected by noise in each of the two phases. Since each of the qubits is noisy, adding more qubits to the system adds more noise. Remarkably, we indeed found that in the disentangling phase the order parameter is unaffected by adding more qubits to the system. This is because, in this phase, the strands of the web are very short, so the probe qubit is only sensitive to the noise of its nearest qubits. In contrast, we found that in the entangling phase, where the strands of the entanglement web stretch longer, the order parameter is very sensitive to the size of the system, or equivalently, the amount of noise in the system. The transition between these two sharply contrasting behaviors indicates a transition in the entanglement character of the system as the “strength” of measurement is increased.

Order parameter vs. gate density (number of entangling operations) for different numbers of qubits. When the number of entangling operations is low, measurements play a larger role in limiting the entanglement across the system. When the number of entangling operations is high, entanglement is widespread, which results in the dependence of the order parameter on system size (inset).

In our experiment, we also demonstrated a novel form of quantum teleportation that arises in the entangling phase. Typically, a specific set of operations are necessary to implement quantum teleportation, but here, the teleportation emerges from the randomness of the non-unitary dynamics. When all qubits, except the probe and another system of far away qubits, are measured, the remaining two systems are strongly entangled with each other. Without measurement, these two systems of qubits would be too far away from each other to know about the existence of each other. With measurements, however, entanglement can be generated faster than the limits typically imposed by locality and causality. This “measurement-induced entanglement” between the qubits (that must also be aided with a classical communications channel) is what allows for quantum teleportation to occur.

Proxy entropy vs. gate density for two far separated subsystems (pink and black qubits) when all other qubits are measured. There is a finite-size crossing at ~0.9. Above this gate density, the probe qubit is entangled with qubits on the opposite side of the system and is a signature of the teleporting phase.


Our experiments demonstrate the effect of measurements on a quantum circuit. We show that by tuning the strength of measurements, we can induce transitions to new phases of quantum entanglement within the system and even generate an emergent form of quantum teleportation. This work could potentially have relevance to quantum computing schemes, where entanglement and measurements both play a role.


This work was done while Jesse Hoke was interning at Google from Stanford University. We would like to thank Katie McCormick, our Quantum Science Communicator, for helping to write this blog post.

Source: Google AI Blog

Developing industrial use cases for physical simulation on future error-corrected quantum computers

If you’ve paid attention to the quantum computing space, you’ve heard the claim that in the future, quantum computers will solve certain problems exponentially more efficiently than classical computers can. They have the potential to transform many industries, from pharmaceuticals to energy.

For the most part, these claims have rested on arguments about the asymptotic scaling of algorithms as the problem size approaches infinity, but this tells us very little about the practical performance of quantum computers for finite-sized problems. We want to be more concrete: Exactly which problems are quantum computers more suited to tackle than their classical counterparts, and exactly what quantum algorithms could we run to solve these problems? Once we’ve designed an algorithm, we can go beyond analysis based on asymptotic scaling — we can determine the actual resources required to compile and run the algorithm on a quantum computer, and how that compares to a classical computation.

Over the last few years, Google Quantum AI has collaborated with industry and academic partners to assess the prospects for quantum simulation to revolutionize specific technologies and perform concrete analyses of the resource requirements. In 2022, we developed quantum algorithms to analyze the chemistry of an important enzyme family called cytochrome P450. Then, in our paper released this fall, we demonstrated how to use a quantum computer to study sustainable alternatives to cobalt for use in lithium ion batteries. And most recently, as we report in a preprint titled “Quantum computation of stopping power for inertial fusion target design,” we’ve found a new application in modeling the properties of materials in inertial confinement fusion experiments, such as those at the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory, which recently made headlines for a breakthrough in nuclear fusion.

Below, we describe these three industrially relevant applications for simulations with quantum computers. While running the algorithms will require an error-corrected quantum computer, which is still years away, working on this now will ensure that we are ready with efficient quantum algorithms when such a quantum computer is built. Already, our work has reduced the cost of compiling and running the algorithms significantly, as we have reported in the past. Our work is essential for demonstrating the potential of quantum computing, but it also provides our hardware team with target specifications for the number of qubits and time needed to run useful quantum algorithms in the future.

Application 1: The CYP450 mechanism

The pharmaceutical industry is often touted as a field ripe for discovery using quantum computers. But concrete examples of such potential applications are few and far between. Working with collaborators at the pharmaceutical company Boehringer Ingelheim, our partners at the startup QSimulate, and academic colleagues at Columbia University, we explored one example in the 2022 PNAS article, “Reliably assessing the electronic structure of cytochrome P450 on today’s classical computers and tomorrow’s quantum computers”.

Cytochrome P450 is an enzyme family naturally found in humans that helps us metabolize drugs. It excels at its job: more than 70% of all drug metabolism is performed by enzymes of the P450 family. The enzymes work by oxidizing the drug — a process that depends on complex correlations between electrons. The details of the interactions are too complicated for scientists to know a priori how effective the enzyme will be on a particular drug.

In the paper, we showed how a quantum computer could approach this problem. The CYP450 metabolic process is a complex chain of reactions with many intermediate changes in the electronic structure of the enzymes throughout. We first use state-of-the-art classical methods to determine the resources required to simulate this problem on a classical computer. Then we imagine implementing a phase-estimation algorithm — which is needed to compute the ground-state energies of the relevant electronic configurations throughout the reaction chain — on a surface-code error-corrected quantum computer.

With a quantum computer, we could follow the chain of changing electronic structure with greater accuracy and fewer resources. In fact, we find that the higher accuracy offered by a quantum computer is needed to correctly resolve the chemistry in this system, so not only will a quantum computer be better, it will be necessary. And as the system size gets bigger, i.e., the more quantum energy levels we include in the simulation, the more the quantum computer wins over the classical computer. Ultimately, we show that a few million physical qubits would be required to reach quantum advantage for this problem.

Left: Example of an electron orbital (red and blue) of a CYP enzyme. More than 60 such orbitals are required to model the CYP system. Right: Comparison of actual runtime (CPU) of various classical techniques (blue) to hypothetical runtime (QPU) of a quantum algorithm (green). The lower slope of the quantum algorithm demonstrates the favorable asymptotic scaling over classical methods. Already at about 20-30 orbitals, we see a crossover to the regime where a quantum algorithm would be more efficient than classical methods.

Application 2: Lithium-ion batteries

Lithium-ion batteries rely on the electrochemical potential difference between two lithium containing materials. One material used today for the cathodes of Li-ion batteries is LiCoO2. Unfortunately, it has drawbacks from a manufacturing perspective. Cobalt mining is expensive, destructive to the environment, and often utilizes unsafe or abusive labor practices. Consequently, many in the field are interested in alternatives to cobalt for lithium-ion cathodes.

In the 1990’s, researchers discovered that nickel could replace cobalt to form LiNiO2 (called “lithium nickel oxide” or “LNO”) for cathodes. While pure LNO was found to be unstable in production, many cathode materials used in the automotive industry today use a high fraction of nickel and hence, resemble LNO. Despite its applications to industry, however, not all of the chemical properties of LNO are understood — even the properties of its ground state remains a subject of debate.

In our recent paper, “Fault tolerant quantum simulation of materials using Bloch orbitals,” we worked with the chemical company, BASF, the molecular modeling startup, QSimulate, and collaborators at Macquarie University in Australia to develop techniques to perform quantum simulations on systems with periodic, regularly spaced atomic structure, such as LNO. We then applied these techniques to design algorithms to study the relative energies of a few different candidate structures of LNO. With classical computers, high accuracy simulations of the quantum wavefunction are considered too expensive to perform. In our work, we found that a quantum computer would need tens of millions of physical qubits to calculate the energies of each of the four candidate ground-state LNO structures. This is out of reach of the first error-corrected quantum computers, but we expect this number to come down with future algorithmic improvements.

Four candidate structures of LNO. In the paper, we consider the resources required to compare the energies of these structures in order to find the ground state of LNO.

Application 3: Fusion reactor dynamics

In our third and most recent example, we collaborated with theorists at Sandia National Laboratories and our Macquarie University collaborators to put our hypothetical quantum computer to the task of simulating dynamics of charged particles in the extreme conditions typical of inertial confinement fusion (ICF) experiments, like those at the National Ignition Facility. In those experiments, high-intensity lasers are focused into a metallic cavity (hohlraum) that holds a target capsule consisting of an ablator surrounding deuterium–tritium fuel. When the lasers heat the inside of the hohlraum, its walls radiate x-rays that compress the capsule, heating the deuterium and tritium inside to 10s of millions of Kelvin. This allows the nucleons in the fuel to overcome their mutual electrostatic repulsion and start fusing into helium nuclei, also called alpha particles.

Simulations of these experiments are computationally demanding and rely on models of material properties that are themselves uncertain. Even testing these models, using methods similar to those in quantum chemistry, is extremely computationally expensive. In some cases, such test calculations have consumed >100 million CPU hours. One of the most expensive and least accurate aspects of the simulation is the dynamics of the plasma prior to the sustained fusion stage (>10s of millions of Kelvin), when parts of the capsule and fuel are a more balmy 100k Kelvin. In this “warm dense matter” regime, quantum correlations play a larger role in the behavior of the system than in the “hot dense matter” regime when sustained fusion takes place.

In our new preprint, “Quantum computation of stopping power for inertial fusion target design”, we present a quantum algorithm to compute the so-called “stopping power” of the warm dense matter in a nuclear fusion experiment. The stopping power is the rate at which a high energy alpha particle slows down due to Coulomb interactions with the surrounding plasma. Understanding the stopping power of the system is vital for optimizing the efficiency of the reactor. As the alpha particle is slowed by the plasma around it, it transfers its energy to the plasma, heating it up. This self-heating process is the mechanism by which fusion reactions sustain the burning plasma. Detailed modeling of this process will help inform future reactor designs.

We estimate that the quantum algorithm needed to calculate the stopping power would require resources somewhere between the P450 application and the battery application. But since this is the first case study on first-principles dynamics (or any application at finite temperature), such estimates are just a starting point and we again expect to find algorithmic improvements to bring this cost down in the future. Despite this uncertainty, it is still certainly better than the classical alternative, for which the only tractable approaches for these simulations are mean-field methods. While these methods incur unknown systematic errors when describing the physics of these systems, they are currently the only meaningful means of performing such simulations.

Left: A projectile (red) passing through a medium (blue) with initial velocity vproj. Right: To calculate the stopping power, we monitor the energy transfer between the projectile and the medium (blue solid line) and determine its average slope (red dashed line).

Discussion and conclusion

The examples described above are just three of a large and growing body of concrete applications for a future error-corrected quantum computer in simulating physical systems. This line of research helps us understand the classes of problems that will most benefit from the power of quantum computing. In particular, the last example is distinct from the other two in that it is simulating a dynamical system. In contrast to the other problems, which focus on finding the lowest energy, static ground state of a quantum system, quantum dynamics is concerned with how a quantum system changes over time. Since quantum computers are inherently dynamic — the qubit states evolve and change as each operation is performed — they are particularly well suited to solving these kinds of problems. Together with collaborators at Columbia, Harvard, Sandia National Laboratories and Macquarie University in Australia we recently published a paper in Nature Communications demonstrating that quantum algorithms for simulating electron dynamics can be more efficient even than approximate, “mean-field” classical calculations, while simultaneously offering much higher accuracy.

Developing and improving algorithms today prepares us to take full advantage of them when an error-corrected quantum computer is eventually realized. Just as in the classical computing case, we expect improvements at every level of the quantum computing stack to further lower the resource requirements. But this first step helps separate hyperbole from genuine applications amenable to quantum computational speedups.


We would like to thank Katie McCormick, our Quantum Science Communicator, for helping to write this blog post.

Source: Google AI Blog

Google Research, 2022 & beyond: Natural sciences

(This is Part 7 in our series of posts covering different topical areas of research at Google. You can find other posts in the series here.)

It's an incredibly exciting time to be a scientist. With the amazing advances in machine learning (ML) and quantum computing, we now have powerful new tools that enable us to act on our curiosity, collaborate in new ways, and radically accelerate progress toward breakthrough scientific discoveries.

Since joining Google Research eight years ago, I’ve had the privilege of being part of a community of talented researchers fascinated by applying cutting-edge computing to push the boundaries of what is possible in applied science. Our teams are exploring topics across the physical and natural sciences. So, for this year’s blog post I want to focus on high-impact advances we’ve made recently in the fields of biology and physics, from helping to organize the world’s protein and genomics information to benefit people's lives to improving our understanding of the nature of the universe with quantum computers. We are inspired by the great potential of this work.

Using machine learning to unlock mysteries in biology

Many of our researchers are fascinated by the extraordinary complexity of biology, from the mysteries of the brain, to the potential of proteins, and to the genome, which encodes the very language of life. We’ve been working alongside scientists from other leading organizations around the world to tackle important challenges in the fields of connectomics, protein function prediction, and genomics, and to make our innovations accessible and useful to the greater scientific community.


One exciting application of our Google-developed ML methods was to explore how information travels through the neuronal pathways in the brains of zebrafish, which provides insight into how the fish engage in social behavior like swarming. In collaboration with researchers from the Max Planck Institute for Biological Intelligence, we were able to computationally reconstruct a portion of zebrafish brains imaged with 3D electron microscopy — an exciting advance in the use of imaging and computational pipelines to map out the neuronal circuitry in small brains, and another step forward in our long-standing contributions to the field of connectomics.

Reconstruction of the neural circuitry of a larval zebrafish brain, courtesy of the Max Planck Institute for Biological Intelligence.

The technical advances necessary for this work will have applications even beyond neuroscience. For example, to address the difficulty of working with such large connectomics datasets, we developed and released TensorStore, an open-source C++ and Python software library designed for storage and manipulation of n-dimensional data. We look forward to seeing the ways it is used in other fields for the storage of large datasets.

We're also using ML to shed light on how human brains perform remarkable feats like language by comparing human language processing and autoregressive deep language models (DLMs). For this study, a collaboration with colleagues at Princeton University and New York University Grossman School of Medicine, participants listened to a 30-minute podcast while their brain activity was recorded using electrocorticography. The recordings suggested that the human brain and DLMs share computational principles for processing language, including continuous next-word prediction, reliance on contextual embeddings, and calculation of post-onset surprise based on word match (we can measure how surprised the human brain is by the word, and correlate that surprise signal with how well the word is predicted by the DLM). These results provide new insights into language processing in the human brain, and suggest that DLMs can be used to reveal valuable insights about the neural basis of language.


ML has also allowed us to make significant advances in understanding biological sequences. In 2022, we leveraged recent advances in deep learning to accurately predict protein function from raw amino acid sequences. We also worked in close collaboration with the European Molecular Biology Laboratory's European Bioinformatics Institute (EMBL-EBI) to carefully assess model performance and add hundreds of millions of functional annotations to the public protein databases UniProt, Pfam/InterPro, and MGnify. Human annotation of protein databases can be a laborious and slow process and our ML methods enabled a giant leap forward — for example, increasing the number of Pfam annotations by a larger number than all other efforts during the past decade combined. The millions of scientists worldwide who access these databases each year can now use our annotations for their research.

Google Research contributions to Pfam exceed in size all expansion efforts made to the database over the last decade.

Although the first draft of the human genome was released in 2003, it was incomplete and had many gaps due to technical limitations in the sequencing technologies. In 2022 we celebrated the remarkable achievements of the Telomere-2-Telomere (T2T) Consortium in resolving these previously unavailable regions — including five full chromosome arms and nearly 200 million base pairs of novel DNA sequences — which are interesting and important for questions of human biology, evolution, and disease. Our open source genomics variant caller, DeepVariant, was one of the tools used by the T2T Consortium to prepare their release of a complete 3.055 billion base pair sequence of a human genome. The T2T Consortium is also using our newer open source method DeepConsensus, which provides on-device error correction for Pacific Biosciences long-read sequencing instruments, in their latest research toward comprehensive pan-genome resources that can represent the breadth of human genetic diversity.

Using quantum computing for new physics discoveries

When it comes to making scientific discoveries, quantum computing is still in its infancy, but has a lot of potential. We’re exploring ways of advancing the capabilities of quantum computing so that it can become a tool for scientific discovery and breakthroughs. In collaboration with physicists from around the world, we are also starting to use our existing quantum computers to create interesting new experiments in physics.

As an example of such experiments, consider the problem where a sensor measures something, and a computer then processes the data from the sensor. Traditionally, this means the sensor’s data is processed as classical information on our computers. Instead, one idea in quantum computing is to directly process quantum data from sensors. Feeding data from quantum sensors directly to quantum algorithms without going through classical measurements may provide a large advantage. In a recent Science paper written in collaboration with researchers from multiple universities, we show that quantum computing can extract information from exponentially fewer experiments than classical computing, as long as the quantum computer is coupled directly to the quantum sensors and is running a learning algorithm. This “quantum machine learning” can yield an exponential advantage in dataset size, even with today’s noisy intermediate-scale quantum computers. Because experimental data is often the limiting factor in scientific discovery, quantum ML has the potential to unlock the vast power of quantum computers for scientists. Even better, the insights from this work are also applicable to learning on the output of quantum computations, such as the output of quantum simulations that may otherwise be difficult to extract.

Even without quantum ML, a powerful application of quantum computers is to experimentally explore quantum systems that would be otherwise impossible to observe or simulate. In 2022, the Quantum AI team used this approach to observe the first experimental evidence of multiple microwave photons in a bound state using superconducting qubits. Photons typically do not interact with one another, and require an additional element of non-linearity to cause them to interact. The results of our quantum computer simulations of these interactions surprised us — we thought the existence of these bound states relied on fragile conditions, but instead we found that they were robust even to relatively strong perturbations that we applied.

Occupation probability versus discrete time step for n-photon bound states. We observe that the majority of the photons (darker colors) remain bound together.

Given the initial successes we have had in applying quantum computing to make physics breakthroughs, we are hopeful about the possibility of this technology to enable future groundbreaking discoveries that could have as significant a societal impact as the creation of transistors or GPS. The future of quantum computing as a scientific tool is exciting!


I would like to thank everyone who worked hard on the advances described in this post, including the Google Applied Sciences, Quantum AI, Genomics and Brain teams and their collaborators across Google Research and externally. Finally, I would like to thank the many Googlers who provided feedback in the writing of this post, including Lizzie Dorfman, Erica Brand, Elise Kleeman, Abe Asfaw, Viren Jain, Lucy Colwell, Andrew Carroll, Ariel Goldstein and Charina Chou.


Google Research, 2022 & beyond

This was the seventh blog post in the “Google Research, 2022 & Beyond” series. Other posts in this series are listed in the table below:

Source: Google AI Blog

Amplification at the Quantum limit

The Google Quantum AI team is building quantum computers with superconducting microwave circuits, but much like a classical computer the superconducting processor at the heart of these computers is only part of the story. An entire technology stack of peripheral hardware is required to make the quantum computer work properly. In many cases these parts must be custom designed, requiring extensive research and development to reach the highest levels of performance.

In this post, we highlight one aspect of this supplemental hardware: our superconducting microwave amplifiers. In “Readout of a Quantum Processor with High Dynamic Range Josephson Parametric Amplifiers”, published in Applied Physics Letters, we describe how we increased the maximum output power of our superconducting microwave amplifiers by a factor of over 100x. We discuss how this work can pave the way for the operation of larger quantum processor chips with improved performance.

Why microwave amplifiers?

One of the challenges of operating a superconducting quantum processor is measuring the state of a qubit without disturbing its operation. Fundamentally, this comes down to a microwave engineering problem, where we need to be able to measure the energy inside the qubit resonator without exposing it to noisy or lossy wiring. This can be accomplished by adding an additional microwave resonator to the system that is coupled to the qubit, but far from the qubit’s resonance frequency. The resonator acts as a filter that isolates the qubit from the control lines but also picks up a state-dependent frequency shift from the qubit. Just like in the binary phase shift keying (BPSK) encoding technique, the digital state of the qubit (0 or 1) is translated into a phase for a probe tone (microwave signal) reflecting off of this auxiliary resonator. Measuring the phase of this probe tone allows us to infer the state of the qubit without directly interfacing with the qubit itself.

While this sounds simple, the qubit actually imposes a severe cap on how much power can be used for this probe tone. In normal operation, a qubit should be in the 0 state or the 1 state or some superposition of the two. A measurement pulse should collapse the qubit into one of these two states, but using too much power can push it into a higher excited state and corrupt the computation. A safe measurement power is typically around -125 dBm, which amounts to only a handful of microwave photons interacting with the processor during the measurement. Typically, small signals are measured using microwave amplifiers, which increase the signal level, but also add their own noise. How much noise is acceptable? If the measurement process takes too long, the qubit state can change due to energy loss in the circuit. This means that these very small signals must be measured in just a few hundred nanoseconds with very high (>99%) fidelity. We therefore cannot afford to average the signal over a longer time to reduce the noise. Unfortunately, even the best semiconductor low-noise amplifiers are still almost a factor of 10 too noisy.

The solution is to design our own custom amplifiers based on the same circuit elements as the qubits themselves. These amplifiers typically consist of Josephson junctions to provide a tunable inductance wired into a superconducting resonant circuit. By constructing a resonant circuit out of these elements, you can create a parametric amplifier where amplification is achieved by modulating the tunable inductance at twice the frequency you want to amplify. Additionally, because all of the wiring is made of lossless superconductors, these devices operate near the quantum limit of added noise, where the only noise in the signal is coming from amplification of the zero point quantum voltage fluctuations.

The one downside to these devices is that the Josephson junctions constrain the power of the signals we can measure. If the signal is too large, the drive current can approach the junction critical current and degrade the amplifier performance. Even if this limit was sufficient to measure a single qubit, our goal was to increase efficiency by measuring up to six qubits at a time using the same amplifier. Some groups get around this limit by making traveling wave amplifiers, where the signals are distributed across thousands of junctions. This increases the saturation power, but the amplifiers get very complicated to produce and take up a lot of space on the chip. Our goal was to create an amplifier that could handle as much power as a traveling wave amplifier but with the same simple and compact design we were used to.


The critical current of each Josephson junction limits our amplifier’s power handling. However, increasing this critical current also changes the inductance and, thus, the operating frequency of the amplifier. To avoid these constraints, we replaced a standard 2-junction DC SQUID with a nonlinear tunable inductor made up of two RF-SQUID arrays in parallel, which we call a snake inductor. Each RF-SQUID consists of a Josephson junction and geometric inductances L1 and L2, and each array contains 20 RF-SQUIDs. In this case, each junction of a standard DC SQUID is replaced by one of these RF-SQUID arrays. While the critical current of each RF-SQUID is much higher, we chain them together to keep the inductance and operating frequency the same. While this is a relatively modest increase in device complexity, it enables us to increase the power handling of each amplifier by roughly a factor of 100x. It is also fully compatible with existing designs that use impedance matching circuits to provide large measurement bandwidth.

Circuit diagram of our superconducting microwave amplifier. A split bias coil allows both DC and RF modulation of the snake inductor, while a shunt capacitor sets the frequency range. The flow of current is illustrated in the animation where an applied current (blue) on the bias line causes a circulating current (red) in the snake. A tapered impedance transformer lowers the loaded Q of the device. Since the Q is defined as frequency divided by bandwidth, lowering the Q with a constant frequency increases the bandwidth of the amplifier. Example circuit parameters used for a real device are Cs=6.0 pF, L1=2.6 pH, L2=8.0 pH, Lb=30 pH, M=50 pH, Z0 = 50 Ohms, and Zfinal = 18 ohms. The device operation is illustrated with a small signal (magenta) reflecting off the input of the amplifier. When the large pump tone (blue) is applied to the bias port, it generates amplified versions of the signal (gold) and a secondary tone known as an idler (also gold).
Microscope image of the nonlinear resonator showing the resonant circuit that consists of a large parallel plate capacitor, nonlinear snake inductor, and a current bias transformer to tune the inductance.

We measure this performance improvement by measuring the saturation power of the amplifier, or the point at which the gain is compressed by 1 dB. We also measure this power value vs. frequency to see how it scales with amplifier gain and distance from the center of the amplifier bandwidth. Since the amplifier gain is symmetric about its center frequency we measure this in terms of absolute detuning, which is just the absolute value of the difference between the center frequency of the amplifier and the probe tone frequency.

Input and output saturation power (1-dB gain compression point), calibrated using a superconducting quantum processor vs. absolute detuning from the amplifier center frequency.

Conclusion and future directions

The new microwave amplifiers represent a big step forward for our qubit measurement system. They will allow us to measure more qubits using a single device, and enable techniques that require higher power for each measurement tone. However, there are still quite a few areas we would like to explore. For example, we are currently investigating the application of snake inductors in amplifiers with advanced impedance matching techniques, directional amplifiers, and non-reciprocal devices like microwave circulators.


We would like to thank the Quantum AI team for the infrastructure and support that enabled the creation and measurement of our microwave amplifier devices. Thanks to our cohort of talented Google Research Interns that contributed to the future work mentioned above: Andrea Iorio for developing algorithms that automatically tune amplifiers and provide a snapshot of the local parameter space, Ryan Kaufman for measuring a new class of amplifiers using multi-pole impedance matching networks, and Randy Kwende for designing and testing a range of parametric devices based on snake inductors. With their contributions, we are gaining a better understanding of our amplifiers and designing the next generation of parametrically-driven devices.

Source: Google AI Blog

Formation of Robust Bound States of Interacting Photons

When quantum computers were first proposed, they were hoped to be a way to better understand the quantum world. With a so-called “quantum simulator,” one could engineer a quantum computer to investigate how various quantum phenomena arise, including those that are intractable to simulate with a classical computer.

But making a useful quantum simulator has been a challenge. Until now, quantum simulations with superconducting qubits have predominantly been used to verify pre-existing theoretical predictions and have rarely explored or discovered new phenomena. Only a few experiments with trapped ions or cold atoms have revealed new insights. Superconducting qubits, even though they are one of the main candidates for universal quantum computing and have demonstrated computational capabilities beyond classical reach, have so far not delivered on their potential for discovery.

In “Formation of Robust Bound States of Interacting Photons”, published in Nature, we describe a previously unpredicted phenomenon first discovered through experimental investigation. First, we present the experimental confirmation of the theoretical prediction of the existence of a composite particle of interacting photons, or a bound state, using the Google Sycamore quantum processor. Second, while studying this system, we discovered that even though one might guess the bound states to be fragile, they remain robust to perturbations that we expected to have otherwise destroyed them. Not only does this open the possibility of designing systems that leverage interactions between photons, it also marks a step forward in the use of superconducting quantum processors to make new scientific discoveries by simulating non-equilibrium quantum dynamics.


Photons, or quanta of electromagnetic radiation like light and microwaves, typically don’t interact. For example, two intersecting flashlight beams will pass through one another undisturbed. In many applications, like telecommunications, the weak interactions of photons is a valuable feature. For other applications, such as computers based on light, the lack of interactions between photons is a shortcoming.

In a quantum processor, the qubits host microwave photons, which can be made to interact through two-qubit operations. This allows us to simulate the XXZ model, which describes the behavior of interacting photons. Importantly, this is one of the few examples of integrable models, i.e., one with a high degree of symmetry, which greatly reduces its complexity. When we implement the XXZ model on the Sycamore processor, we observe something striking: the interactions force the photons into bundles known as bound states.

Using this well-understood model as a starting point, we then push the study into a less-understood regime. We break the high level of symmetries displayed in the XXZ model by adding extra sites that can be occupied by the photons, making the system no longer integrable. While this nonintegrable regime is expected to exhibit chaotic behavior where bound states dissolve into their usual, solitary selves, we instead find that they survive!

Bound Photons

To engineer a system that can support the formation of bound states, we study a ring of superconducting qubits that host microwave photons. If a photon is present, the value of the qubit is “1”, and if not, the value is “0”. Through the so-called “fSim” quantum gate, we connect neighboring sites, allowing the photons to hop around and interact with other photons on the nearest-neighboring sites.

Superconducting qubits can be occupied or unoccupied with microwave photons. The “fSim” gate operation allows photons to hop and interact with each other. The corresponding unitary evolution has a hopping term between two sites (orange) and an interaction term corresponding to an added phase when two adjacent sites are occupied by a photon.
We implement the fSim gate between neighboring qubits (left) to effectively form a ring of 24 interconnected qubits on which we simulate the behavior of the interacting photons (right).

The interactions between the photons affect their so-called “phase.” This phase keeps track of the oscillation of the photon’s wavefunction. When the photons are non-interacting, their phase accumulation is rather uninteresting. Like a well-rehearsed choir, they’re all in sync with one another. In this case, a photon that was initially next to another photon can hop away from its neighbor without getting out of sync. Just as every person in the choir contributes to the song, every possible path the photon can take contributes to the photon’s overall wavefunction. A group of photons initially clustered on neighboring sites will evolve into a superposition of all possible paths each photon might have taken.

When photons interact with their neighbors, this is no longer the case. If one photon hops away from its neighbor, its rate of phase accumulation changes, becoming out of sync with its neighbors. All paths in which the photons split apart overlap, leading to destructive interference. It would be like each choir member singing at their own pace — the song itself gets washed out, becoming impossible to discern through the din of the individual singers. Among all the possible configuration paths, the only possible scenario that survives is the configuration in which all photons remain clustered together in a bound state. This is why interaction can enhance and lead to the formation of a bound state: by suppressing all other possibilities in which photons are not bound together.

Left: Evolution of interacting photons forming a bound state. Right: Time goes from left to right, each path represents one of the paths that can break the 2-photon bonded state. Due to interactions, these paths interfere destructively, preventing the photons from splitting apart.
Occupation probability versus gate cycle, or discrete time step, for n-photon bound states. We prepare bound states of varying sizes and watch them evolve. We observe that the majority of the photons (darker colors) remain bound together.

In our processor, we start by putting two to five photons on adjacent sites (i.e., initializing two to five adjacent qubits in “1”, and the remaining qubits in “0”), and then study how they propagate. First, we notice that in the theoretically predicted parameter regime, they remain stuck together. Next, we find that the larger bound states move more slowly around the ring, consistent with the fact that they are “heavier”. This can be seen in the plot above where the lattice sites closest to Site 12, the initial position of the photons, remain darker than the others with increasing number of photons (nph) in the bound state, indicating that with more photons bound together there is less propagation around the ring.

Bound States Behave Like Single Composite Particles

To more rigorously show that the bound states indeed behave as single particles with well-defined physical properties, we devise a method to measure how the energy of the particles changes with momentum, i.e., the energy-momentum dispersion relation.

To measure the energy of the bound state, we use the fact that the energy difference between two states determines how fast their relative phase grows with time. Hence, we prepare the bound state in a superposition with the state that has no photons, and measure their phase difference as a function of time and space. Then, to convert the result of this measurement to a dispersion relation, we utilize a Fourier transform, which translates position and time into momentum and energy, respectively. We’re left with the familiar energy-momentum relationship of excitations in a lattice.

Spectroscopy of bound states. We compare the phase accumulation of an n-photon bound state with that of the vacuum (no photons) as a function of lattice site and time. A 2D Fourier transform yields the dispersion relation of the bound-state quasiparticle.

Breaking Integrability

The above system is “integrable,” meaning that it has a sufficient number of conserved quantities that its dynamics are constrained to a small part of the available computational space. In such integrable regimes, the appearance of bound states is not that surprising. In fact, bound states in similar systems were predicted in 2012, then observed in 2013. However, these bound states are fragile and their existence is usually thought to derive from integrability. For more complex systems, there is less symmetry and integrability is quickly lost. Our initial idea was to probe how these bound states disappear as we break integrability to better understand their rigidity.

To break integrability, we modify which qubits are connected with fSim gates. We add qubits so that at alternating sites, in addition to hopping to each of its two nearest-neighboring sites, a photon can also hop to a third site oriented radially outward from the ring.

While a bound state is constrained to a very small part of phase space, we expected that the chaotic behavior associated with integrability breaking would allow the system to explore the phase space more freely. This would cause the bound states to break apart. We find that this is not the case. Even when the integrability breaking is so strong that the photons are equally likely to hop to the third site as they are to hop to either of the two adjacent ring sites, the bound state remains intact, up to the decoherence effect that makes them slowly decay (see paper for details).

Top: New geometry to break integrability. Alternating sites are connected to a third site oriented radially outward. This increases the complexity of the system, and allows for potentially chaotic behavior. Bottom: Despite this added complexity pushing the system beyond integrability, we find that the 3-photon bound state remains stable even for a relatively large perturbation. The probability of remaining bound decreases slowly due to decoherence (see paper).


We don’t yet have a satisfying explanation for this unexpected resilience. We speculate that it may be related to a phenomenon called prethermalization, where incommensurate energy scales in the system can prevent a system from reaching thermal equilibrium as quickly as it otherwise would. We believe further investigations will hopefully lead to new insights into many-body quantum physics, including the interplay of prethermalization and integrability.


We would like to thank our Quantum Science Communicator Katherine McCormick for her help writing this blog post.

Source: Google AI Blog

Quantum Advantage in Learning from Experiments

In efforts to learn about the quantum world, scientists face a big obstacle: their classical experience of the world. Whenever a quantum system is measured, the act of this measurement destroys the “quantumness” of the state. For example, if the quantum state is in a superposition of two locations, where it can seem to be in two places at the same time, once it is measured, it will randomly appear either ”here” or “there”, but not both. We only ever see the classical shadows cast by this strange quantum world.

A growing number of experiments are implementing machine learning (ML) algorithms to aid in analyzing data, but these have the same limitations as the people they aim to help: They can’t directly access and learn from quantum information. But what if there were a quantum machine learning algorithm that could directly interact with this quantum data?

In “Quantum Advantage in Learning from Experiments”, a collaboration with researchers at Caltech, Harvard, Berkeley, and Microsoft published in Science, we show that a quantum learning agent can perform exponentially better than a classical learning agent at many tasks. Using Google’s quantum computer, Sycamore, we demonstrate the tremendous advantage that a quantum machine learning (QML) algorithm has over the best possible classical algorithm. Unlike previous quantum advantage demonstrations, no advances in classical computing power could overcome this gap. This is the first demonstration of a provable exponential advantage in learning about quantum systems that is robust even on today's noisy hardware.

Quantum Speedup
QML combines the best of both quantum computing and the lesser-known field of quantum sensing.

Quantum computers will likely offer exponential improvements over classical systems for certain problems, but to realize their potential, researchers first need to scale up the number of qubits and to improve quantum error correction. What’s more, the exponential speed-up over classical algorithms promised by quantum computers relies on a big, unproven assumption about so-called “complexity classes” of problems — namely, that the class of problems that can be solved on a quantum computer is larger than those that can be solved on a classical computer.. It seems like a reasonable assumption, and yet, no one has proven it. Until it's proven, every claim of quantum advantage will come with an asterisk: that it can do better than any known classical algorithm.

Quantum sensors, on the other hand, are already being used for some high-precision measurements and offer modest (and proven) advantages over classical sensors. Some quantum sensors work by exploiting quantum correlations between particles to extract more information about a system than it otherwise could have. For example, scientists can use a collection of N atoms to measure aspects of the atoms’ environment like the surrounding magnetic fields. Typically the sensitivity to the field that the atoms can measure scales with the square root of N. But if one uses quantum entanglement to create a complex web of correlations between the atoms, then one can improve the scaling to be proportional to N. But as with most quantum sensing protocols, this quadratic speed-up over classical sensors is the best one can ever do.

Enter QML, a technology that straddles the line between quantum computers and quantum sensors. QML algorithms make computations that are aided by quantum data. Instead of measuring the quantum state, a quantum computer can store quantum data and implement a QML algorithm to process the data without collapsing it. And when this data is limited, a QML algorithm can squeeze exponentially more information out of each piece it receives when considering particular tasks.

Comparison of a classical machine learning algorithm and a quantum machine learning algorithm. The classical machine learning algorithm measures a quantum system, then performs classical computations on the classical data it acquires to learn about the system. The quantum machine learning algorithm, on the other hand, interacts with the quantum states produced by the system, giving it a quantum advantage over the CML.

To see how a QML algorithm works, it’s useful to contrast with a standard quantum experiment. If a scientist wants to learn about a quantum system, they might send in a quantum probe, such as an atom or other quantum object whose state is sensitive to the system of interest, let it interact with the system, then measure the probe. They can then design new experiments or make predictions based on the outcome of the measurements. Classical machine learning (CML) algorithms follow the same process using an ML model, but the operating principle is the same — it’s a classical device processing classical information.

A QML algorithm instead uses an artificial “quantum learner.” After the quantum learner sends in a probe to interact with the system, it can choose to store the quantum state rather than measure it. Herein lies the power of QML. It can collect multiple copies of these quantum probes, then entangle them to learn more about the system faster.

Suppose, for example, the system of interest produces a quantum superposition state probabilistically by sampling from some distribution of possible states. Each state is composed of n quantum bits, or qubits, where each is a superposition of “0” and “1” — all learners are allowed to know the generic form of the state, but must learn its details.

In a standard experiment, where only classical data is accessible, every measurement provides a snapshot of the distribution of quantum states, but since it’s only a sample, it is necessary to measure many copies of the state to reconstruct it. In fact, it will take on the order of 2n copies.

A QML agent is more clever. By saving a copy of the n-qubit state, then entangling it with the next copy that comes along, it can learn about the global quantum state more quickly, giving a better idea of what the state looks like sooner.

Basic schematic of the QML algorithm. Two copies of a quantum state are saved, then a “Bell measurement” is performed, where each pair is entangled and their correlations measured.

The classical reconstruction is like trying to find an image hiding in a sea of noisy pixels — it could take a very long time to average-out all the noise to know what the image is representing. The quantum reconstruction, on the other hand, uses quantum mechanics to isolate the true image faster by looking for correlations between two different images at once.

To better understand the power of QML, we first looked at three different learning tasks and theoretically proved that in each case, the quantum learning agent would do exponentially better than the classical learning agent. Each task was related to the example given above:

  1. Learning about incompatible observables of the quantum state — i.e., observables that cannot be simultaneously known to arbitrary precision due to the Heisenberg uncertainty principle, like position and momentum. But we showed that this limit can be overcome by entangling multiple copies of a state.
  2. Learning about the dominant components of the quantum state. When noise is present, it can disturb the quantum state. But typically the “principal component” — the part of the superposition with the highest probability — is robust to this noise, so we can still glean information about the original state by finding this dominant part.
  3. Learning about a physical process that acts on a quantum system or probe. Sometimes the state itself is not the object of interest, but a physical process that evolves this state is. We can learn about various fields and interactions by analyzing the evolution of a state over time.

In addition to the theoretical work, we ran some proof-of-principle experiments on the Sycamore quantum processor. We started by implementing a QML algorithm to perform the first task. We fed an unknown quantum mixed state to the algorithm, then asked which of two observables of the state was larger. After training the neural network with simulation data, we found that the quantum learning agent needed exponentially fewer experiments to reach a prediction accuracy of 70% — equating to 10,000 times fewer measurements when the system size was 20 qubits. The total number of qubits used was 40 since two copies were stored at once.

Experimental comparison of QML vs. CML algorithms for predicting a quantum state’s observables. While the number of experiments needed to achieve 70% accuracy with a CML algorithm (“C” above) grows exponentially with the size of the quantum state n, the number of experiments the QML algorithm (“Q”) needs is only linear in n. The dashed line labeled “Rigorous LB (C)” represents the theoretical lower bound (LB) — the best possible performance — of a classical machine learning algorithm.

In a second experiment, relating to the task 3 above, we had the algorithm learn about the symmetry of an operator that evolves the quantum state of their qubits. In particular, if a quantum state might undergo evolution that is either totally random or random but also time-reversal symmetric, it can be difficult for a classical learner to tell the difference. In this task, the QML algorithm can separate the operators into two distinct categories, representing two different symmetry classes, while the CML algorithm fails outright. The QML algorithm was completely unsupervised, so this gives us hope that the approach could be used to discover new phenomena without needing to know the right answer beforehand.

Experimental comparison of QML vs. CML algorithms for predicting the symmetry class of an operator. While QML successfully separates the two symmetry classes, the CML fails to accomplish the task.

This experimental work represents the first demonstrated exponential advantage in quantum machine learning. And, distinct from a computational advantage, when limiting the number of samples from the quantum state, this type of quantum learning advantage cannot be challenged, even by unlimited classical computing resources.

So far, the technique has only been used in a contrived, “proof-of-principle” experiment, where the quantum state is deliberately produced and the researchers pretend not to know what it is. To use these techniques to make quantum-enhanced measurements in a real experiment, we’ll first need to work on current quantum sensor technology and methods to faithfully transfer quantum states to a quantum computer. But the fact that today’s quantum computers can already process this information to squeeze out an exponential advantage in learning bodes well for the future of quantum machine learning.

We would like to thank our Quantum Science Communicator Katherine McCormick for writing this blog post. Images reprinted with permission from Huang et al., Science, Vol 376:1182 (2022).

Source: Google AI Blog

Hybrid Quantum Algorithms for Quantum Monte Carlo

The intersection between the computational difficulty and practical importance of quantum chemistry challenges run on quantum computers has long been a focus for Google Quantum AI. We’ve experimentally simulated simple models of chemical bonding, high-temperature superconductivity, nanowires, and even exotic phases of matter such as time crystals on our Sycamore quantum processors. We’ve also developed algorithms suitable for the error-corrected quantum computers we aim to build, including the world’s most efficient algorithm for large-scale quantum computations of chemistry (in the usual way of formulating the problem) and a pioneering approach that allows for us to solve the same problem at an extremely high spatial resolution by encoding the position of the electrons differently.

Despite these successes, it is still more effective to use classical algorithms for studying quantum chemistry than the noisy quantum processors we have available today. However, when the laws of quantum mechanics are translated into programs that a classical computer can run, we often find that the amount of time or memory required scales very poorly with the size of the physical system to simulate.

Today, in collaboration with Dr. Joonho Lee and Professor David Reichmann at Colombia, we present the Nature publication “Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer”, where we propose and experimentally validate a new way of combining classical and quantum computation to study chemistry, which can replace a computationally-expensive subroutine in a powerful classical algorithm with a “cheaper”, noisy, calculation on a small quantum computer. To evaluate the performance of this hybrid quantum-classical approach, we applied this idea to perform the largest quantum computation of chemistry to date, using 16 qubits to study the forces experienced by two carbon atoms in a diamond crystal. Not only was this experiment four qubits larger than our earlier chemistry calculations on Sycamore, we were also able to use a more comprehensive description of the physics that fully incorporated the interactions between electrons.

Google’s Sycamore quantum processor. Photo Credit: Rocco Ceselin.

A New Way of Combining Quantum and Classical
Our starting point was to use a family of Monte Carlo techniques (projector Monte Carlo, more on that below) to give us a useful description of the lowest energy state of a quantum mechanical system (like the two carbon atoms in a crystal mentioned above). However, even just storing a good description of a quantum state (the “wavefunction”) on a classical computer can be prohibitively expensive, let alone calculating one.

Projector Monte Carlo methods provide a way around this difficulty. Instead of writing down a full description of the state, we design a set of rules for generating a large number of oversimplified descriptions of the state (for example, lists of where each electron might be in space) whose average is a good approximation to the real ground state. The “projector” in projector Monte Carlo refers to how we design these rules — by continuously trying to filter out the incorrect answers using a mathematical process called projection, similar to how a silhouette is a projection of a three-dimensional object onto a two-dimensional surface.

Unfortunately, when it comes to chemistry or materials science, this idea isn’t enough to find the ground state on its own. Electrons belong to a class of particles known as fermions, which have a surprising quantum mechanical quirk to their behavior. When two identical fermions swap places, the quantum mechanical wavefunction (the mathematical description that tells us everything there is to know about them) picks up a minus sign. This minus sign gives rise to the famous Pauli exclusion principle (the fact that two fermions cannot occupy the same state). It can also cause projector Monte Carlo calculations to become inefficient or even break down completely. The usual resolution to this fermion sign problem involves tweaking the Monte Carlo algorithm to include some information from an approximation to the ground state. By using an approximation (even a crude one) to the lowest energy state as a guide, it is usually possible to avoid breakdowns and even obtain accurate estimates of the properties of the true ground state.

Top: An illustration of how the fermion sign problem appears in some cases. Instead of following the blue line curve, our estimates of the energy follow the red curve and become unstable. Bottom: An example of the improvements we might see when we try to fix the sign problem. By using a quantum computer, we hope to improve the initial guess that guides our calculation and obtain a more accurate answer.

For the most challenging problems (such as modeling the breaking of chemical bonds), the computational cost of using an accurate enough initial guess on a classical computer can be too steep to afford, which led our collaborator Dr. Joonho Lee to ask if a quantum computer could help. We had already demonstrated in previous experiments that we can use our quantum computer to approximate the ground state of a quantum system. In these earlier experiments we aimed to measure quantities (such as the energy of the state) that are directly linked to physical properties (like the rate of a chemical reaction). In this new hybrid algorithm, we instead needed to make a very different kind of measurement: quantifying how far the states generated by the Monte Carlo algorithm on our classical computer are from those prepared on the quantum computer. Using some recently developed techniques, we were even able to do all of the measurements on the quantum computer before we ran the Monte Carlo algorithm, separating the quantum computer’s job from the classical computer’s.

A diagram of our calculation. The quantum processor (right) measures information that guides the classical calculation (left). The crosses indicate the qubits, with the ones used for the largest experiment shaded green. The direction of the arrows indicate that the quantum processor doesn’t need any feedback from the classical calculation. The red bars represent the parts of the classical calculation that are filtered out by the data from the quantum computer in order to avoid the fermion sign problem and get a good estimate of properties like the energy of the ground state.

This division of labor between the classical and the quantum computer helped us make good use of both resources. Using our Sycamore quantum processor, we prepared a kind of approximation to the ground state that would be difficult to scale up classically. With a few hours of time on the quantum device, we extracted all of the data we needed to run the Monte Carlo algorithm on the classical computer. Even though the data was noisy (like all present-day quantum computations), it had enough signal that it was able to guide the classical computer towards a very accurate reconstruction of the true ground state (shown in the figure below). In fact, we showed that even when we used a low-resolution approximation to the ground state on the quantum computer (just a few qubits encoding the position of the electrons), the classical computer could efficiently solve a much higher resolution version (with more realism about where the electrons can be).

Top left: a diagram showing the sixteen qubits we used for our largest experiment. Bottom left: an illustration of the carbon atoms in a diamond crystal. Our calculation focused on two atoms (the two that are highlighted in translucent yellow). Right: A plot showing how the error in the total energy (closer to zero is better) changes as we adjust the lattice constant (the spacing between the two carbon atoms). Many properties we might care about, such as the structure of the crystal, can be determined by understanding how the energy varies as we move the atoms around. The calculations we performed using the quantum computer (red points) are comparable in accuracy to two state-of-the-art classical methods (yellow and green triangles) and are extremely close to the numbers we would have gotten if we had a perfect quantum computer rather than a noisy one (black points). The fact that these red and black points are so close tells us that the error in our calculation comes from using an approximate ground state on the quantum computer that was too simple, not from being overwhelmed by noise on the device.

Using our new hybrid quantum algorithm, we performed the largest ever quantum computation of chemistry or materials science. We used sixteen qubits to calculate the energy of two carbon atoms in a diamond crystal. This experiment was four qubits larger than our first chemistry calculations on Sycamore, we obtained more accurate results, and we were able to use a better model of the underlying physics. By guiding a powerful classical Monte Carlo calculation using data from our quantum computer, we performed these calculations in a way that was naturally robust to noise.

We’re optimistic about the promise of this new research direction and excited to tackle the challenge of scaling these kinds of calculations up towards the boundary of what we can do with classical computing, and even to the hard-to-study corners of the universe. We know the road ahead of us is long, but we’re excited to have another tool in our growing toolbox.

I’d like to thank my co-authors on the manuscript, Bryan O’Gorman, Nicholas Rubin, David Reichman, Ryan Babbush, and especially Joonho Lee for their many contributions, as well as Charles Neill and Pedram Rousham for their help executing the experiment. I’d also like to thank the larger Google Quantum AI team, who designed, built, programmed, and calibrated the Sycamore processor.

Source: Google AI Blog