Tag Archives: Quantum AI

Achieving Precision in Quantum Material Simulations

In fall of 2019, we demonstrated that the Sycamore quantum processor could outperform the most powerful classical computers when applied to a tailor-made problem. The next challenge is to extend this result to solve practical problems in materials science, chemistry and physics. But going beyond the capabilities of classical computers for these problems is challenging and will require new insights to achieve state-of-the-art accuracy. Generally, the difficulty in performing quantum simulations of such physical problems is rooted in the wave nature of quantum particles, where deviations in the initial setup, interference from the environment, or small errors in the calculations can lead to large deviations in the computational result.

In two upcoming publications, we outline a blueprint for achieving record levels of precision for the task of simulating quantum materials. In the first work, we consider one-dimensional systems, like thin wires, and demonstrate how to accurately compute electronic properties, such as current and conductance. In the second work, we show how to map the Fermi-Hubbard model, which describes interacting electrons, to a quantum processor in order to simulate important physical properties. These works take a significant step towards realizing our long-term goal of simulating more complex systems with practical applications, like batteries and pharmaceuticals.

A bottom view of one of the quantum dilution refrigerators during maintenance. During the operation, the microwave wires that are floating in this image are connected to the quantum processor, e.g., the Sycamore chip, bringing the temperature of the lowest stage to a few tens of milli-degrees above absolute zero temperature.

Computing Electronic Properties of Quantum Materials
In “Accurately computing electronic properties of a quantum ring”, to be published in Nature, we show how to reconstruct key electronic properties of quantum materials. The focus of this work is on one-dimensional conductors, which we simulate by forming a loop out of 18 qubits on the Sycamore processor in order to mimic a very narrow wire. We illustrate the underlying physics through a series of simple text-book experiments, starting with a computation of the “band-structure” of this wire, which describes the relationship between the energy and momentum of electrons in the metal. Understanding such structure is a key step in computing electronic properties such as current and conductance. Despite being an 18-qubit algorithm consisting of over 1,400 logical operations, a significant computational task for near-term devices, we are able to achieve a total error as low as 1%.

The key insight enabling this level of accuracy stems from robust properties of the Fourier transform. The quantum signal that we measure oscillates in time with a small number of frequencies. Taking a Fourier transform of this signal reveals peaks at the oscillation frequencies (in this case, the energy of electrons in the wire). While experimental imperfections affect the height of the observed peaks (corresponding to the strength of the oscillation), the center frequencies are robust to these errors. On the other hand, the center frequencies are especially sensitive to the physical properties of the wire that we hope to study (e.g., revealing small disorders in the local electric field felt by the electrons). The essence of our work is that studying quantum signals in the Fourier domain enables robust protection against experimental errors while providing a sensitive probe of the underlying quantum system.

(Left) Schematic of the 54-qubit quantum processor, Sycamore. Qubits are shown as gray crosses and tunable couplers as blue squares. Eighteen of the qubits are isolated to form a ring. (Middle) Fourier transform of the measured quantum signal. Peaks in the Fourier spectrum correspond to the energy of electrons in the ring. Each peak can be associated with a traveling wave that has fixed momentum. (Right) The center frequency of each peak (corresponding to the energy of electrons in the wire) is plotted versus the peak index (corresponding to the momentum). The measured relationship between energy and momentum is referred to as the ‘band structure’ of the quantum wire and provides valuable information about electronic properties of the material, such as current and conductance.

Quantum Simulation of the Fermi-Hubbard Model
In “Observation of separated dynamics of charge and spin in the Fermi-Hubbard model”, we focus on the dynamics of interacting electrons. Interactions between particles give rise to novel phenomena such as high temperature superconductivity and spin-charge separation. The simplest model that captures this behavior is known as the Fermi-Hubbard model. In materials such as metals, the atomic nuclei form a crystalline lattice and electrons hop from lattice site to lattice site carrying electrical current. In order to accurately model these systems, it is necessary to include the repulsion that electrons feel when getting close to one another. The Fermi-Hubbard model captures this physics with two simple parameters that describe the hopping rate (J) and the repulsion strength (U).

We realize the dynamics of this model by mapping the two physical parameters to logical operations on the qubits of the processor. Using these operations, we simulate a state of the electrons where both the electron charge and spin densities are peaked near the center of the qubit array. As the system evolves, the charge and spin densities spread at different rates due to the strong correlations between electrons. Our results provide an intuitive picture of interacting electrons and serve as a benchmark for simulating quantum materials with superconducting qubits.

(Left top) Illustration of the one-dimensional Fermi-Hubbard model in a periodic potential. Electrons are shown in blue, with their spin indicated by the connected arrow. J, the distance between troughs in the electric potential field, reflects the “hopping” rate, i.e., the rate at which electrons transition from one trough in the potential to another, and U, the amplitude, represents the strength of repulsion between electrons. (Left bottom) The simulation of the model on a qubit ladder, where each qubit (square) represents a fermionic state with spin-up or spin-down (arrows). (Right) Time evolution of the model reveals separated spreading rates of charge and spin. Points and solid lines represent experimental and numerical exact results, respectively. At t = 0, the charge and spin densities are peaked at the middle sites. At later times, the charge density spreads and reaches the boundaries faster than the spin density.

Conclusion
Quantum processors hold the promise to solve computationally hard tasks beyond the capability of classical approaches. However, in order for these engineered platforms to be considered as serious contenders, they must offer computational accuracy beyond the current state-of-the-art classical methods. In our first experiment, we demonstrate an unprecedented level of accuracy in simulating simple materials, and in our second experiment, we show how to embed realistic models of interacting electrons into a quantum processor. It is our hope that these experimental results help progress the goal of moving beyond the classical computing horizon.

Source: Google AI Blog


Quantum Machine Learning and the Power of Data

Quantum computing has rapidly advanced in both theory and practice in recent years, and with it the hope for the potential impact in real applications. One key area of interest is how quantum computers might affect machine learning. We recently demonstrated experimentally that quantum computers are able to naturally solve certain problems with complex correlations between inputs that can be incredibly hard for traditional, or “classical”, computers. This suggests that learning models made on quantum computers may be dramatically more powerful for select applications, potentially boasting faster computation, better generalization on less data, or both. Hence it is of great interest to understand in what situations such a “quantum advantage” might be achieved.

The idea of quantum advantage is typically phrased in terms of computational advantages. That is, given some task with well defined inputs and outputs, can a quantum computer achieve a more accurate result than a classical machine in a comparable runtime? There are a number of algorithms for which quantum computers are suspected to have overwhelming advantages, such as Shor’s factoring algorithm for factoring products of large primes (relevant to RSA encryption) or the quantum simulation of quantum systems. However, the difficulty of solving a problem, and hence the potential advantage for a quantum computer, can be greatly impacted by the availability of data. As such, understanding when a quantum computer can help in a machine learning task depends not only on the task, but also the data available, and a complete understanding of this must include both.

In “Power of data in quantum machine learning”, published in Nature Communications, we dissect the problem of quantum advantage in machine learning to better understand when it will apply. We show how the complexity of a problem formally changes with the availability of data, and how this sometimes has the power to elevate classical learning models to be competitive with quantum algorithms. We then develop a practical method for screening when there may be a quantum advantage for a chosen set of data embeddings in the context of kernel methods. We use the insights from the screening method and learning bounds to introduce a novel method that projects select aspects of feature maps from a quantum computer back into classical space. This enables us to imbue the quantum approach with additional insights from classical machine learning that shows the best empirical separation in quantum learning advantages to date.

Computational Power of Data
The idea of quantum advantage over a classical computer is often framed in terms of computational complexity classes. Examples such as factoring large numbers and simulating quantum systems are classified as bounded quantum polynomial time (BQP) problems, which are those thought to be handled more easily by quantum computers than by classical systems. Problems easily solved on classical computers are called bounded probabilistic polynomial (BPP) problems.

We show that learning algorithms equipped with data from a quantum process, such as a natural process like fusion or chemical reactions, form a new class of problems (which we call BPP/Samp) that can efficiently perform some tasks that traditional algorithms without data cannot, and is a subclass of the problems efficiently solvable with polynomial sized advice (P/poly). This demonstrates that for some machine learning tasks, understanding the quantum advantage requires examination of available data as well.


Geometric Test for Quantum Learning Advantage

Informed by the results that the potential for advantage changes depending on the availability of data, one may ask how a practitioner can quickly evaluate if their problem may be well suited for a quantum computer. To help with this, we developed a workflow for assessing the potential for advantage within a kernel learning framework. We examined a number of tests, the most powerful and informative of which was a novel geometric test we developed.

In quantum machine learning methods, such as quantum neural networks or quantum kernel methods, a quantum program is often divided into two parts, a quantum embedding of the data (an embedding map for the feature space using a quantum computer), and the evaluation of a function applied to the data embedding. In the context of quantum computing, quantum kernel methods make use of traditional kernel methods, but use the quantum computer to evaluate part or all of the kernel on the quantum embedding, which has a different geometry than a classical embedding. It was conjectured that a quantum advantage might arise from the quantum embedding, which might be much better suited to a particular problem than any accessible classical geometry.

We developed a quick and rigorous test that can be used to quickly compare a particular quantum embedding, kernel, and data set to a range of classical kernels and assess if there is any opportunity for quantum advantage across, e.g., possible label functions such as those used for image recognition tasks. We define a geometric constant g, which quantifies the amount of data that could theoretically close that gap, based on the geometric test. This is an extremely useful technique for deciding, based on data constraints, if a quantum solution is right for the given problem.

Projected Quantum Kernel Approach
One insight revealed by the geometric test, was that existing quantum kernels often suffered from a geometry that was easy to best classically because they encouraged memorization, instead of understanding. This inspired us to develop a projected quantum kernel, in which the quantum embedding is projected back to a classical representation. While this representation is still hard to compute with a classical computer directly, it comes with a number of practical advantages in comparison to staying in the quantum space entirely.

Geometric quantity g, which quantifies the potential for quantum advantage, depicted for several embeddings, including the projected quantum kernel introduced here.

By selectly projecting back to classical space, we can retain aspects of the quantum geometry that are still hard to simulate classically, but now it is much easier to develop distance functions, and hence kernels, that are better behaved with respect to modest changes in the input than was the original quantum kernel. In addition the projected quantum kernel facilitates better integration with powerful non-linear kernels (like a squared exponential) that have been developed classically, which is much more challenging to do in the native quantum space.

This projected quantum kernel has a number of benefits over previous approaches, including an improved ability to describe non-linear functions of the existing embedding, a reduction in the resources needed to process the kernel from quadratic to linear with the number of data points, and the ability to generalize better at larger sizes. The kernel also helps to expand the geometric g, which helps to ensure the greatest potential for quantum advantage.

Data Sets Exhibit Learning Advantages
The geometric test quantifies potential advantage for all possible label functions, however in practice we are most often interested in specific label functions. Using learning theoretic approaches, we also bound the generalization error for specific tasks, including those which are definitively quantum in origin. As the advantage of a quantum computer relies on its ability to use many qubits simultaneously but previous approaches scale poorly in number of qubits, it is important to verify the tasks at reasonably large qubit sizes ( > 20 ) to ensure a method has the potential to scale to real problems. For our studies we verified up to 30 qubits, which was enabled by the open source tool, TensorFlow-Quantum, enabling scaling to petaflops of compute.

Interestingly, we showed that many naturally quantum problems, even up to 30 qubits, were readily handled by classical learning methods when sufficient data were provided. Hence one conclusion is that even for some problems that look quantum, classical machine learning methods empowered by data can match the power of quantum computers. However, using the geometric construction in combination with the projected quantum kernel, we were able to construct a data set that exhibited an empirical learning advantage for a quantum model over a classical one. Thus, while it remains an open question to find such data sets in natural problems, we were able to show the existence of label functions where this can be the case. Although this problem was engineered and a quantum computational advantage would require the embeddings to be larger and more challenging, this work represents an important step in understanding the role data plays in quantum machine learning.

Prediction accuracy as a function of the number of qubits (n) for a problem engineered to maximize the potential for learning advantage in a quantum model. The data is shown for two different sizes of training data (N).

For this problem, we scaled up the number of qubits (n) and compared the prediction accuracy of the projected quantum kernel to existing kernel approaches and the best classical machine learning model in our dataset. Moreover, a key takeaway from these results is that although we showed the existence of datasets where a quantum computer has an advantage, for many quantum problems, classical learning methods were still the best approach. Understanding how data can affect a given problem is a key factor to consider when discussing quantum advantage in learning problems, unlike traditional computation problems for which that is not a consideration.

Conclusions
When considering the ability of quantum computers to aid in machine learning, we have shown that the availability of data fundamentally changes the question. In our work, we develop a practical set of tools for examining these questions, and use them to develop a new projected quantum kernel method that has a number of advantages over existing approaches. We build towards the largest numerical demonstration to date, 30 qubits, of potential learning advantages for quantum embeddings. While a complete computational advantage on a real world application remains to be seen, this work helps set the foundation for the path forward. We encourage any interested readers to check out both the paper and related TensorFlow-Quantum tutorials that make it easy to build on this work.

Acknowledgements
We would like to acknowledge our co-authors on this paper — Michael Broughton, Masoud Mohseni, Ryan Babbush, Sergio Boixo, and Hartmut Neven, as well as the entirety of the Google Quantum AI team. In addition, we acknowledge valuable help and feedback from Richard Kueng, John Platt, John Preskill, Thomas Vidick, Nathan Wiebe, Chun-Ju Wu, and Balint Pato.


1Current affiliation — Institute for Quantum Information and Matter and Department of Computing and Mathematical Sciences, Caltech, Pasadena, CA, USA

Source: Google AI Blog


Scaling Up Fundamental Quantum Chemistry Simulations on Quantum Hardware

Accurate computational prediction of chemical processes from the quantum mechanical laws that govern them is a tool that can unlock new frontiers in chemistry, improving a wide variety of industries. Unfortunately, the exact solution of quantum chemical equations for all but the smallest systems remains out of reach for modern classical computers, due to the exponential scaling in the number and statistics of quantum variables. However, by using a quantum computer, which by its very nature takes advantage of unique quantum mechanical properties to handle calculations intractable to its classical counterpart, simulations of complex chemical processes can be achieved. While today’s quantum computers are powerful enough for a clear computational advantage at some tasks, it is an open question whether such devices can be used to accelerate our current quantum chemistry simulation techniques.

In “Hartree-Fock on a Superconducting Qubit Quantum Computer”, appearing today in Science, the Google AI Quantum team explores this complex question by performing the largest chemical simulation performed on a quantum computer to date. In our experiment, we used a noise-robust variational quantum eigensolver (VQE) to directly simulate a chemical mechanism via a quantum algorithm. Though the calculation focused on the Hartree-Fock approximation of a real chemical system, it was twice as large as previous chemistry calculations on a quantum computer, and contained ten times as many quantum gate operations. Importantly, we validate that algorithms being developed for currently available quantum computers can achieve the precision required for experimental predictions, revealing pathways towards realistic simulations of quantum chemical systems. Furthermore, we have released the code for the experiment, which uses OpenFermion, our open source repository for quantum computations of chemistry.

Google’s Sycamore processor mounted in a cryostat, recently used to demonstrate quantum supremacy and the largest quantum chemistry simulation on a quantum computer. Photo Credit: Rocco Ceselin

Developing an Error Robust Quantum Algorithm for Chemistry
There are a number of ways to use a quantum computer to simulate the ground state energy of a molecular system. In this work we focused on a quantum algorithm “building block”, or circuit primitive, and perfect its performance through a VQE (more on that later). In the classical setting this circuit primitive is equivalent to the Hartree-Fock model and is an important circuit component of an algorithm we previously developed for optimal chemistry simulations. This allows us to focus on scaling up without incurring exponential simulation costs to validate our device. Therefore, robust error mitigation on this component is crucial for accurate simulations when scaling to the “beyond classical” regime.

Errors in quantum computation emerge from interactions of the quantum circuitry with the environment, causing erroneous logic operations — even minor temperature fluctuations can cause qubit errors. Algorithms for simulating chemistry on near-term quantum devices must account for these errors with low overhead, both in terms of the number of qubits or additional quantum resources, such as implementing a quantum error correcting code. The most popular method to account for errors (and why we used it for our experiment) is to use a VQE. For our experiment, we selected the VQE we developed a few years ago, which treats the quantum processor like an neural network and attempts to optimize a quantum circuit’s parameters to account for noisy quantum logic by minimizing a cost function. Just like how classical neural networks can tolerate imperfections in data by optimization, a VQE dynamically adjusts quantum circuit parameters to account for errors that occur during the quantum computation.

Enabling High Accuracy with Sycamore
The experiment was run on the Sycamore processor that was recently used to demonstrate quantum supremacy. Though our experiment required fewer qubits, even higher quantum gate fidelity was needed to resolve chemical bonding. This led to the development of new, targeted calibration techniques that optimally amplify errors so they can be diagnosed and corrected.

Energy predictions of molecular geometries by the Hartree-Fock model simulated on 10 qubits of the Sycamore processor.

Errors in the quantum computation can originate from a variety of sources in the quantum hardware stack. Sycamore has 54-qubits and consists of over 140 individually tunable elements, each controlled with high-speed, analog electrical pulses. Achieving precise control over the whole device requires fine tuning more than 2,000 control parameters, and even small errors in these parameters can quickly add up to large errors in the total computation.

To accurately control the device, we use an automated framework that maps the control problem onto a graph with thousands of nodes, each of which represent a physics experiment to determine a single unknown parameter. Traversing this graph takes us from basic priors about the device to a high fidelity quantum processor, and can be done in less than a day. Ultimately, these techniques along with the algorithmic error mitigation enabled orders of magnitude reduction in the errors.

Left: The energy of a linear chain of Hydrogen atoms as the bond distance between each atom is increased. The solid line is the Hartree-Fock simulation with a classical computer while the points are computed with the Sycamore processor. Right: Two accuracy metrics (infidelity and mean absolute error) for each point computed with Sycamore. “Raw” is the non-error-mitigated data from Sycamore. “+PS” is data from a type of error mitigation correcting the number of electrons. “+Purification” is a type of error mitigation correcting for the right kind of state. “+VQE” is the combination of all the error mitigation along with variational relaxation of the circuit parameters. Experiments on H8, H10, and H12 show similar performance improvements upon error mitigation.

Pathways Forward
We hope that this experiment serves as a blueprint for how to run chemistry calculations on quantum processors, and as a jumping off point on the path to physical simulation advantage. One exciting prospect is that it is known how to modify the quantum circuits used in this experiment in a simple way such that they are no longer efficiently simulable, which would determine new directions for improved quantum algorithms and applications. We hope that the results from this experiment can be used to explore this regime by the broader research community. To run these experiments, you can find the code here.

Source: Google AI Blog


Quantum Supremacy Using a Programmable Superconducting Processor



Physicists have been talking about the power of quantum computing for over 30 years, but the questions have always been: will it ever do something useful and is it worth investing in? For such large-scale endeavors it is good engineering practice to formulate decisive short-term goals that demonstrate whether the designs are going in the right direction. So, we devised an experiment as an important milestone to help answer these questions. This experiment, referred to as a quantum supremacy experiment, provided direction for our team to overcome the many technical challenges inherent in quantum systems engineering to make a computer that is both programmable and powerful. To test the total system performance we selected a sensitive computational benchmark that fails if just a single component of the computer is not good enough.

Today we published the results of this quantum supremacy experiment in the Nature article, “Quantum Supremacy Using a Programmable Superconducting Processor”. We developed a new 54-qubit processor, named “Sycamore”, that is comprised of fast, high-fidelity quantum logic gates, in order to perform the benchmark testing. Our machine performed the target computation in 200 seconds, and from measurements in our experiment we determined that it would take the world’s fastest supercomputer 10,000 years to produce a similar output.
Left: Artist's rendition of the Sycamore processor mounted in the cryostat. (Full Res Version; Forest Stearns, Google AI Quantum Artist in Residence) Right: Photograph of the Sycamore processor. (Full Res Version; Erik Lucero, Research Scientist and Lead Production Quantum Hardware)
The Experiment
To get a sense of how this benchmark works, imagine enthusiastic quantum computing neophytes visiting our lab in order to run a quantum algorithm on our new processor. They can compose algorithms from a small dictionary of elementary gate operations. Since each gate has a probability of error, our guests would want to limit themselves to a modest sequence with about a thousand total gates. Assuming these programmers have no prior experience, they might create what essentially looks like a random sequence of gates, which one could think of as the “hello world” program for a quantum computer. Because there is no structure in random circuits that classical algorithms can exploit, emulating such quantum circuits typically takes an enormous amount of classical supercomputer effort.

Each run of a random quantum circuit on a quantum computer produces a bitstring, for example 0000101. Owing to quantum interference, some bitstrings are much more likely to occur than others when we repeat the experiment many times. However, finding the most likely bitstrings for a random quantum circuit on a classical computer becomes exponentially more difficult as the number of qubits (width) and number of gate cycles (depth) grow.
Process for demonstrating quantum supremacy.
In the experiment, we first ran random simplified circuits from 12 up to 53 qubits, keeping the circuit depth constant. We checked the performance of the quantum computer using classical simulations and compared with a theoretical model. Once we verified that the system was working, we ran random hard circuits with 53 qubits and increasing depth, until reaching the point where classical simulation became infeasible.
Estimate of the equivalent classical computation time assuming 1M CPU cores for quantum supremacy circuits as a function of the number of qubits and number of cycles for the Schrödinger-Feynman algorithm. The star shows the estimated computation time for the largest experimental circuits.
This result is the first experimental challenge against the extended Church-Turing thesis, which states that classical computers can efficiently implement any “reasonable” model of computation. With the first quantum computation that cannot reasonably be emulated on a classical computer, we have opened up a new realm of computing to be explored.

The Sycamore Processor
The quantum supremacy experiment was run on a fully programmable 54-qubit processor named “Sycamore.” It’s comprised of a two-dimensional grid where each qubit is connected to four other qubits. As a consequence, the chip has enough connectivity that the qubit states quickly interact throughout the entire processor, making the overall state impossible to emulate efficiently with a classical computer.

The success of the quantum supremacy experiment was due to our improved two-qubit gates with enhanced parallelism that reliably achieve record performance, even when operating many gates simultaneously. We achieved this performance using a new type of control knob that is able to turn off interactions between neighboring qubits. This greatly reduces the errors in such a multi-connected qubit system. We made further performance gains by optimizing the chip design to lower crosstalk, and by developing new control calibrations that avoid qubit defects.

We designed the circuit in a two-dimensional square grid, with each qubit connected to four other qubits. This architecture is also forward compatible for the implementation of quantum error-correction. We see our 54-qubit Sycamore processor as the first in a series of ever more powerful quantum processors.
Heat map showing single- (e1; crosses) and two-qubit (e2; bars) Pauli errors for all qubits operating simultaneously. The layout shown follows the distribution of the qubits on the processor. (Courtesy of Nature magazine.)

Testing Quantum Physics
To ensure the future utility of quantum computers, we also needed to verify that there are no fundamental roadblocks coming from quantum mechanics. Physics has a long history of testing the limits of theory through experiments, since new phenomena often emerge when one starts to explore new regimes characterized by very different physical parameters. Prior experiments showed that quantum mechanics works as expected up to a state-space dimension of about 1000. Here, we expanded this test to a size of 10 quadrillion and find that everything still works as expected. We also tested fundamental quantum theory by measuring the errors of two-qubit gates and finding that this accurately predicts the benchmarking results of the full quantum supremacy circuits. This shows that there is no unexpected physics that might degrade the performance of our quantum computer. Our experiment therefore provides evidence that more complex quantum computers should work according to theory, and makes us feel confident in continuing our efforts to scale up.

Applications
The Sycamore quantum computer is fully programmable and can run general-purpose quantum algorithms. Since achieving quantum supremacy results last spring, our team has already been working on near-term applications, including quantum physics simulation and quantum chemistry, as well as new applications in generative machine learning, among other areas.

We also now have the first widely useful quantum algorithm for computer science applications: certifiable quantum randomness. Randomness is an important resource in computer science, and quantum randomness is the gold standard, especially if the numbers can be self-checked (certified) to come from a quantum computer. Testing of this algorithm is ongoing, and in the coming months we plan to implement it in a prototype that can provide certifiable random numbers.

What’s Next?
Our team has two main objectives going forward, both towards finding valuable applications in quantum computing. First, in the future we will make our supremacy-class processors available to collaborators and academic researchers, as well as companies that are interested in developing algorithms and searching for applications for today’s NISQ processors. Creative researchers are the most important resource for innovation — now that we have a new computational resource, we hope more researchers will enter the field motivated by trying to invent something useful.

Second, we’re investing in our team and technology to build a fault-tolerant quantum computer as quickly as possible. Such a device promises a number of valuable applications. For example, we can envision quantum computing helping to design new materials — lightweight batteries for cars and airplanes, new catalysts that can produce fertilizer more efficiently (a process that today produces over 2% of the world’s carbon emissions), and more effective medicines. Achieving the necessary computational capabilities will still require years of hard engineering and scientific work. But we see a path clearly now, and we’re eager to move ahead.

Acknowledgements
We’d like to thank our collaborators and contributors — University of California Santa Barbara, NASA Ames Research Center, Oak Ridge National Laboratory, Forschungszentrum Jülich, and many others who helped along the way.


Source: Google AI Blog


On the Path to Cryogenic Control of Quantum Processors



Building a quantum computer that can solve practical problems that would otherwise be classically intractable due to the computation complexity, cost, energy consumption or time to solution, is the longstanding goal of the Google AI Quantum team. Current thresholds suggest a first generation error-corrected quantum computer will require on the order of 1 million physical qubits, which is more than four orders of magnitude more qubits than exist in Bristlecone, our 72 qubit quantum processor. Increasing the number of physical qubits needed for a fault-tolerant quantum computer while maintaining high-quality control of each qubit are intertwined and exciting technological challenges that will require inventions beyond simply copying and pasting our current control architecture. One critical challenge is reducing the number of input/output control lines per qubit by relocating the room temperature analog control electronics to the 3 kelvin stage in the cryostat, while maintaining high-quality qubit control.

As a step towards solving that challenge, this week we presented our first generation cryogenic-CMOS single-qubit controller at the International Solid State Circuits Conference in San Francisco. Fabricated using commercial CMOS technology, our controller operates at 3 kelvin, consumes less than 2 milliwatts of power and measures just 1 mm by 1.6 mm. Functionally, it provides an instruction set for single-qubit gate operations, providing analog control of a qubit via digital lines between room temperature and 3 kelvin, all while consuming ~1000 times less power compared to our current room temperature control electronics.
Google’s first generation cryogenic-CMOS single-qubit controller (center and zoomed on the right) packaged and ready to be deployed inside our cryostat. The controller measures 1mm by 1.6mm.
How to Control 72 Qubits
In our lab in Santa Barbara, we run programs on Bristlecone by applying gigahertz frequency analog control signals to each of the qubits to manipulate the qubit state, to entangle qubits and to measure the outcomes of our computations. How well we define the shape and frequency of these control signals directly impacts the quality of our computation. To make high-quality qubit control signals, we leverage technology developed for smartphones packaged in server racks at room temperature. Individual coaxial cables deliver these signals to each qubit, which are themselves kept inside a cryostat chilled to 10 millikelvin. While this approach makes sense for a Bristlecone-scale quantum processor, which demands 2 control lines per qubit for 144 unique control signals, we realized that a more integrated approach would be required in order to scale our systems to the million qubit level.
Research Scientist Amit Vainsencher checking the wiring on Bristlecone in one of Google's flagship cryostats. Blue coaxial cables are connected from custom analog control electronics (server rack on the right) to the quantum processor.
In our current setup, the number of physical wires connected from room temperature to the qubits inside the cryostat and the finite cooling power of the cryostat represent a significant constraint. One way to alleviate this is to move the digital to analog control closer to the quantum processor. Currently, our room temperature digital-to-analog waveform generators used to control individual qubits, dissipate ~1 watt of waste heat per qubit. The cooling power of our cryostat at 3 kelvin is 0.1 watt. That means if we crammed 150 waveform generators into our cryostat (never mind the limited physical space inside the refrigerator for a moment) we would overwhelm the cooling power of our cryostat by 1500x, thereby cooking our cryostat and rendering our qubits useless. Therefore, simply installing our existing digital-to-analog control in the cryostat will not set us on the path to control millions of qubits. It is clear we need an integrated low-power qubit control solution.

A Cool Idea
In collaboration with University of Massachusetts Professor Joseph Bardin, we set out to develop custom integrated circuits (ICs) to control our qubits from within the cryostat to ultimately reduce the physical I/O connections to and from our future quantum processors. These ICs would be designed to operate in the ultracold environment, specifically 3 kelvin, and turn digital instructions into analog control pulses for qubits. A key research objective was to first design a custom IC with low power requirements, in order to prevent warming up the cryostat.

We designed our IC to dissipate no more than 2 milliwatts of power at 3 kelvin, which can be challenging as most physical CMOS models assume operation closer to 300 kelvin. After design and fabrication of the IC with the low power design constraints in mind, we verified that the cryogenic-CMOS qubit controller worked at room temperature. We then mounted it in our cryostat at 3 kelvin and connected it to a qubit (mounted at 10 millikelvin in the same cryostat). We carried out a series of experiments to establish that the cryogenic-CMOS qubit controller worked as designed, and most importantly, that we hadn't just installed a heater inside our cryostat.
Schematic of the cryogenic-CMOS qubit controller mounted on the 3 kelvin stage of our dilution refrigerator and connected to a qubit. Our standard qubit control electronics were connected in parallel to enable control and measurement of the qubit as an in-situ check experiment.
Performance at Low Temperature
Baseline experiments for our new quantum control hardware, including T1, Rabi oscillations, and single qubit gates, show similar performance compared to our standard room-temperature qubit control electronics: qubit coherence time was virtually unchanged, and high-visibility Rabi oscillations were observed by varying the amplitude of the pulses out of the cryogenic-CMOS qubit controller—a signature response of a driven qubit.

Comparison of the qubit coherence time measured using the standard and cryogenic quantum controllers.
Measured Rabi amplitude oscillations using the cryogenic controller. The green and black traces are the probability of measuring the qubits in the 1 and 0 states, respectively.
Next Steps
Although all of these results are promising, this first generation cryogenic-CMOS qubit controller is but one small step towards a truly scalable qubit control and measurement system. For instance, our controller is only able to address a single qubit, and it still requires several connections to room temperature. In addition, we still need to work hard to quantify the error rates for single qubit gates. As such, we are excited to reduce the energy required to control qubits and still maintain the delicate control required to perform high-quality qubit operations.

Acknowledgements
This work was carried out with the support of the Google Visiting Researcher Program while Prof. Bardin, an Associate Professor with the University of Massachusetts Amherst, was on sabbatical with the Google AI Quantum Team. This work would not have been possible without the many contributions of members of the Google AI Quantum team, especially Evan Jeffrey for his integration of the cryo-CMOS controller into the qubit calibration software, Ted White for his on-demand qubit calibrations and Trent Huang for his tireless design rules checks.

Source: Google AI Blog


Exploring Quantum Neural Networks



Since its inception, the Google AI Quantum team has pushed to understand the role of quantum computing in machine learning. The existence of algorithms with provable advantages for global optimization suggest that quantum computers may be useful for training existing models within machine learning more quickly, and we are building experimental quantum computers to investigate how intricate quantum systems can carry out these computations. While this may prove invaluable, it does not yet touch on the tantalizing idea that quantum computers might be able to provide a way to learn more about complex patterns in physical systems that conventional computers cannot in any reasonable amount of time.

Today we talk about two recent papers from the Google AI Quantum team that make progress towards understanding the power of quantum computers for learning tasks. The first constructs a quantum model of neural networks to investigate how a popular classification task might be carried out on quantum processors. In the second paper, we show how peculiar features of quantum geometry change the strategies for training these networks in comparison to their classical counterparts, and offer guidance towards more robust training of these networks.

In “Classification with Quantum Neural Networks on Near Term Processors”, we construct a model of quantum neural networks (QNNs) that is specifically designed to work on quantum processors that are expected to be available in the near term. While the current work is primarily theoretical, their structure facilitates implementation and testing on quantum computers in the immediate future. These QNNs can be adapted through supervised learning of labeled data, and we show that it is possible to train a QNN to classify images in the famous MNIST dataset. Follow up work in this area with larger quantum devices may pit the ability of quantum networks to learn patterns against popular classical networks.
Quantum Neural Network for classification. Here we depict a sample quantum neural network, where in contrast to hidden layers in classical deep neural networks, the boxes represent entangling actions, or “quantum gates”, on qubits. In a superconducting qubit setup this could be enacted through a microwave control pulse corresponding to each box.
In “Barren Plateaus in Quantum Neural Network Training Landscapes”, we focus on the training of quantum neural networks, and probe questions related to a key difficulty in classical neural networks, which is the problem of vanishing or exploding gradients. In conventional neural networks, a good unbiased initial guess for the neuron weights often involves randomization, although there can be some difficulties as well. Our paper shows that peculiar features of quantum geometry unequivocally prevent this from being a good strategy in the quantum case, instead taking you to barren plateaus. The implications of this work may guide future strategies for initializing and training quantum neural networks.
QNN vanishing gradient: concentration of measure in high dimensional spaces. In very high dimensional spaces, such as those explored by quantum computers, the vast majority of states counterintuitively sit near the equator of the hypersphere (left). This means that any smooth function on this space will tend to take a value very close to its mean with overwhelming probability when selected at random (right).
This research sets the stage for improvements in both the construction and training of quantum neural networks. In particular, experimental realizations of quantum neural networks using hardware at Google will enable rapid exploration of quantum neural networks in the near term. We hope that the insights from the geometry of these states will lead to new algorithms to train these networks that will be essential to unlocking their full potential.

Source: Google AI Blog


Understanding Performance Fluctuations in Quantum Processors



One area of research the Google AI Quantum team pursues is building quantum processors from superconducting electrical circuits, which are attractive candidates for implementing quantum bits (qubits). While superconducting circuits have demonstrated state-of-the-art performance and extensibility to modest processor sizes comprising tens of qubits, an outstanding challenge is stabilizing their performance, which can fluctuate unpredictably. Although performance fluctuations have been observed in numerous superconducting qubit architectures, their origin isn’t well understood, impeding progress in stabilizing processor performance.

In “Fluctuations of Energy-Relaxation Times in Superconducting Qubits” published in this week’s Physical Review Letters, we use qubits as probes of their environment to show that performance fluctuations are dominated by material defects. This was done by investigating qubits’ energy relaxation times (T1) — a popular performance metric that gives the length of time that it takes for a qubit to undergo energy-relaxation from its excited to ground state — as a function of operating frequency and time.

In measuring T1, we found that some qubit operating frequencies are significantly worse than others, forming energy-relaxation hot-spots (see figure below). Our research suggests that these hot spots are due to material defects, which are themselves quantum systems that can extract energy from qubits when their frequencies overlap (i.e. are “resonant”). Surprisingly, we found that the energy-relaxation hot spots are not static, but “move” on timescales ranging from minutes to hours. From these observations, we concluded that the dynamics of defects’ frequencies into and out of resonance with qubits drives the most significant performance fluctuations.
Left: A quantum processor similar to the one that was used to investigate qubit performance fluctuations. One qubit is highlighted in blue. Right: One qubit’s energy-relaxation time “T1” plotted as a function of it’s operating frequency and time. We see energy-relaxation hotspots, which our data suggest are due to material defects (black arrowheads). The motion of these hotspots into and out-of resonance with the qubit are responsible for the most significant energy-relaxation fluctuations. Note that these data were taken over a frequency band with an above-average density of defects.
These defects — which are typically referred to as two-level-systems (TLS) — are commonly believed to exist at the material interfaces of superconducting circuits. However, even after decades of research, their microscopic origin still puzzles researchers. In addition to clarifying the origin of qubit performance fluctuations, our data shed light on the physics governing defect dynamics, which is an important piece of this puzzle. Interestingly, from thermodynamics arguments we would not expect the defects that we see to exhibit any dynamics at all. Their energies are about one order of magnitude higher than the thermal energy available in our quantum processor, and so they should be “frozen out.” The fact that they are not frozen out suggests their dynamics may be driven by interactions with other defects that have much lower energies and can thus be thermally activated.

The fact that qubits can be used to investigate individual material defects - which are believed to have atomic dimensions, millions of times smaller than our qubits - demonstrates that they are powerful metrological tools. While it’s clear that defect research could help address outstanding problems in materials physics, it’s perhaps surprising that it has direct implications on improving the performance of today’s quantum processors. In fact, defect metrology already informs our processor design and fabrication, and even the mathematical algorithms that we use to avoid defects during quantum processor runtime. We hope this research motivates further work into understanding material defects in superconducting circuits.

Source: Google AI Blog


Announcing Cirq: An Open Source Framework for NISQ Algorithms



Over the past few years, quantum computing has experienced a growth not only in the construction of quantum hardware, but also in the development of quantum algorithms. With the availability of Noisy Intermediate Scale Quantum (NISQ) computers (devices with ~50 - 100 qubits and high fidelity quantum gates), the development of algorithms to understand the power of these machines is of increasing importance. However, a common problem when designing a quantum algorithm on a NISQ processor is how to take full advantage of these limited quantum devices—using resources to solve the hardest part of the problem rather than on overheads from poor mappings between the algorithm and hardware. Furthermore some quantum processors have complex geometric constraints and other nuances, and ignoring these will either result in faulty quantum computation, or a computation that is modified and sub-optimal.*

Today at the First International Workshop on Quantum Software and Quantum Machine Learning (QSML), the Google AI Quantum team announced the public alpha of Cirq, an open source framework for NISQ computers. Cirq is focused on near-term questions and helping researchers understand whether NISQ quantum computers are capable of solving computational problems of practical importance. Cirq is licensed under Apache 2, and is free to be modified or embedded in any commercial or open source package.
Once installed, Cirq enables researchers to write quantum algorithms for specific quantum processors. Cirq gives users fine tuned control over quantum circuits, specifying gate behavior using native gates, placing these gates appropriately on the device, and scheduling the timing of these gates within the constraints of the quantum hardware. Data structures are optimized for writing and compiling these quantum circuits to allow users to get the most out of NISQ architectures. Cirq supports running these algorithms locally on a simulator, and is designed to easily integrate with future quantum hardware or larger simulators via the cloud.
We are also announcing the release of OpenFermion-Cirq, an example of a Cirq based application enabling near-term algorithms. OpenFermion is a platform for developing quantum algorithms for chemistry problems, and OpenFermion-Cirq is an open source library which compiles quantum simulation algorithms to Cirq. The new library uses the latest advances in building low depth quantum algorithms for quantum chemistry problems to enable users to go from the details of a chemical problem to highly optimized quantum circuits customized to run on particular hardware. For example, this library can be used to easily build quantum variational algorithms for simulating properties of molecules and complex materials.

Quantum computing will require strong cross-industry and academic collaborations if it is going to realize its full potential. In building Cirq, we worked with early testers to gain feedback and insight into algorithm design for NISQ computers. Below are some examples of Cirq work resulting from these early adopters:
To learn more about how Cirq is helping enable NISQ algorithms, please visit the links above where many of the adopters have provided example source code for their implementations.

Today, the Google AI Quantum team is using Cirq to create circuits that run on Google’s Bristlecone processor. In the future, we plan to make this processor available in the cloud, and Cirq will be the interface in which users write programs for this processor. In the meantime, we hope Cirq will improve the productivity of NISQ algorithm developers and researchers everywhere. Please check out the GitHub repositories for Cirq and OpenFermion-Cirq — pull requests welcome!

Acknowledgements
We would like to thank Craig Gidney for leading the development of Cirq, Ryan Babbush and Kevin Sung for building OpenFermion-Cirq and a whole host of code contributors to both frameworks.


* An analogous situation is how early classical programmers needed to run complex programs in very small memory spaces by paying careful attention to the lowest level details of the hardware.

Source: Google AI Blog


The Question of Quantum Supremacy



Quantum computing integrates the two largest technological revolutions of the last half century, information technology and quantum mechanics. If we compute using the rules of quantum mechanics, instead of binary logic, some intractable computational tasks become feasible. An important goal in the pursuit of a universal quantum computer is the determination of the smallest computational task that is prohibitively hard for today’s classical computers. This crossover point is known as the “quantum supremacy” frontier, and is a critical step on the path to more powerful and useful computations.

In “Characterizing quantum supremacy in near-term devices” published in Nature Physics (arXiv here), we present the theoretical foundation for a practical demonstration of quantum supremacy in near-term devices. It proposes the task of sampling bit-strings from the output of random quantum circuits, which can be thought of as the “hello world” program for quantum computers. The upshot of the argument is that the output of random chaotic systems (think butterfly effect) become very quickly harder to predict the longer they run. If one makes a random, chaotic qubit system and examines how long a classical system would take to emulate it, one gets a good measure of when a quantum computer could outperform a classical one. Arguably, this is the strongest theoretical proposal to prove an exponential separation between the computational power of classical and quantum computers.

Determining where exactly the quantum supremacy frontier lies for sampling random quantum circuits has rapidly become an exciting area of research. On one hand, improvements in classical algorithms to simulate quantum circuits aim to increase the size of the quantum circuits required to establish quantum supremacy. This forces an experimental quantum device with a sufficiently large number of qubits and low enough error rates to implement circuits of sufficient depth (i.e the number of layers of gates in the circuit) to achieve supremacy. On the other hand, we now understand better how the particular choice of the quantum gates used to build random quantum circuits affects the simulation cost, leading to improved benchmarks for near-term quantum supremacy (available for download here), which are in some cases quadratically more expensive to simulate classically than the original proposal.

Sampling from random quantum circuits is an excellent calibration benchmark for quantum computers, which we call cross-entropy benchmarking. A successful quantum supremacy experiment with random circuits would demonstrate the basic building blocks for a large-scale fault-tolerant quantum computer. Furthermore, quantum physics has not yet been tested for highly complex quantum states such as this.
Space-time volume of a quantum circuit computation. The computational cost for quantum simulation increases with the volume of the quantum circuit, and in general grows exponentially with the number of qubits and the circuit depth. For asymmetric grids of qubits, the computational space-time volume grows slower with depth than for symmetric grids, and can result in circuits exponentially easier to simulate.
In “A blueprint for demonstrating quantum supremacy with superconducting qubits” (arXiv here), we illustrate a blueprint towards quantum supremacy and experimentally demonstrate a proof-of-principle version for the first time. In the paper, we discuss two key ingredients for quantum supremacy: exponential complexity and accurate computations. We start by running algorithms on subsections of the device ranging from 5 to 9 qubits. We find that the classical simulation cost grows exponentially with the number of qubits. These results are intended to provide a clear example of the exponential power of these devices. Next, we use cross-entropy benchmarking to compare our results against that of an ordinary computer and show that our computations are highly accurate. In fact, the error rate is low enough to achieve quantum supremacy with a larger quantum processor.

Beyond achieving quantum supremacy, a quantum platform should offer clear applications. In our paper, we apply our algorithms towards computational problems in quantum statistical-mechanics using complex multi-qubit gates (as opposed to the two-qubit gates designed for a digital quantum processor with surface code error correction). We show that our devices can be used to study fundamental properties of materials, e.g. microscopic differences between metals and insulators. By extending these results to next-generation devices with ~50 qubits, we hope to answer scientific questions that are beyond the capabilities of any other computing platform.
Photograph of two gmon superconducting qubits and their tunable coupler developed by Charles Neill and Pedram Roushan.
These two publications introduce a realistic proposal for near-term quantum supremacy, and demonstrate a proof-of-principle version for the first time. We will continue to decrease the error rates and increase the number of qubits in quantum processors to reach the quantum supremacy frontier, and to develop quantum algorithms for useful near-term applications.

The Question of Quantum Supremacy



Quantum computing integrates the two largest technological revolutions of the last half century, information technology and quantum mechanics. If we compute using the rules of quantum mechanics, instead of binary logic, some intractable computational tasks become feasible. An important goal in the pursuit of a universal quantum computer is the determination of the smallest computational task that is prohibitively hard for today’s classical computers. This crossover point is known as the “quantum supremacy” frontier, and is a critical step on the path to more powerful and useful computations.

In “Characterizing quantum supremacy in near-term devices” published in Nature Physics (arXiv here), we present the theoretical foundation for a practical demonstration of quantum supremacy in near-term devices. It proposes the task of sampling bit-strings from the output of random quantum circuits, which can be thought of as the “hello world” program for quantum computers. The upshot of the argument is that the output of random chaotic systems (think butterfly effect) become very quickly harder to predict the longer they run. If one makes a random, chaotic qubit system and examines how long a classical system would take to emulate it, one gets a good measure of when a quantum computer could outperform a classical one. Arguably, this is the strongest theoretical proposal to prove an exponential separation between the computational power of classical and quantum computers.

Determining where exactly the quantum supremacy frontier lies for sampling random quantum circuits has rapidly become an exciting area of research. On one hand, improvements in classical algorithms to simulate quantum circuits aim to increase the size of the quantum circuits required to establish quantum supremacy. This forces an experimental quantum device with a sufficiently large number of qubits and low enough error rates to implement circuits of sufficient depth (i.e the number of layers of gates in the circuit) to achieve supremacy. On the other hand, we now understand better how the particular choice of the quantum gates used to build random quantum circuits affects the simulation cost, leading to improved benchmarks for near-term quantum supremacy (available for download here), which are in some cases quadratically more expensive to simulate classically than the original proposal.

Sampling from random quantum circuits is an excellent calibration benchmark for quantum computers, which we call cross-entropy benchmarking. A successful quantum supremacy experiment with random circuits would demonstrate the basic building blocks for a large-scale fault-tolerant quantum computer. Furthermore, quantum physics has not yet been tested for highly complex quantum states such as this.
Space-time volume of a quantum circuit computation. The computational cost for quantum simulation increases with the volume of the quantum circuit, and in general grows exponentially with the number of qubits and the circuit depth. For asymmetric grids of qubits, the computational space-time volume grows slower with depth than for symmetric grids, and can result in circuits exponentially easier to simulate.
In “A blueprint for demonstrating quantum supremacy with superconducting qubits” (arXiv here), we illustrate a blueprint towards quantum supremacy and experimentally demonstrate a proof-of-principle version for the first time. In the paper, we discuss two key ingredients for quantum supremacy: exponential complexity and accurate computations. We start by running algorithms on subsections of the device ranging from 5 to 9 qubits. We find that the classical simulation cost grows exponentially with the number of qubits. These results are intended to provide a clear example of the exponential power of these devices. Next, we use cross-entropy benchmarking to compare our results against that of an ordinary computer and show that our computations are highly accurate. In fact, the error rate is low enough to achieve quantum supremacy with a larger quantum processor.

Beyond achieving quantum supremacy, a quantum platform should offer clear applications. In our paper, we apply our algorithms towards computational problems in quantum statistical-mechanics using complex multi-qubit gates (as opposed to the two-qubit gates designed for a digital quantum processor with surface code error correction). We show that our devices can be used to study fundamental properties of materials, e.g. microscopic differences between metals and insulators. By extending these results to next-generation devices with ~50 qubits, we hope to answer scientific questions that are beyond the capabilities of any other computing platform.
Photograph of two gmon superconducting qubits and their tunable coupler developed by Charles Neill and Pedram Roushan.
These two publications introduce a realistic proposal for near-term quantum supremacy, and demonstrate a proof-of-principle version for the first time. We will continue to decrease the error rates and increase the number of qubits in quantum processors to reach the quantum supremacy frontier, and to develop quantum algorithms for useful near-term applications.

Source: Google AI Blog