Tag Archives: Quantum Computing

Scaling Up Fundamental Quantum Chemistry Simulations on Quantum Hardware

Posted by Nicholas Rubin and Charles Neill, Research Scientists, Google AI Quantum

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


Announcing TensorFlow Quantum: An Open Source Library for Quantum Machine Learning

Posted by Alan Ho, Product Lead and Masoud Mohseni, Technical Lead, Google Research

“Nature isn’t classical, damnit, so if you want to make a simulation of nature, you’d better make it quantum mechanical.” — Physicist Richard Feynman

Machine learning (ML), while it doesn’t exactly simulate systems in nature, has the ability to learn a model of a system and predict the system’s behavior. Over the past few years, classical ML models have shown promise in tackling challenging scientific issues, leading to advancements in image processing for cancer detection, forecasting earthquake aftershocks, predicting extreme weather patterns, and detecting new exoplanets. With the recent progress in the development of quantum computing, the development of new quantum ML models could have a profound impact on the world’s biggest problems, leading to breakthroughs in the areas of medicine, materials, sensing, and communications. However, to date there has been a lack of research tools to discover useful quantum ML models that can process quantum data and execute on quantum computers available today.

Today, in collaboration with the University of Waterloo, X, and Volkswagen, we announce the release of TensorFlow Quantum (TFQ), an open-source library for the rapid prototyping of quantum ML models. TFQ provides the tools necessary for bringing the quantum computing and machine learning research communities together to control and model natural or artificial quantum systems; e.g. Noisy Intermediate Scale Quantum (NISQ) processors with ~50 - 100 qubits.

Under the hood, TFQ integrates Cirq with TensorFlow, and offers high-level abstractions for the design and implementation of both discriminative and generative quantum-classical models by providing quantum computing primitives compatible with existing TensorFlow APIs, along with high-performance quantum circuit simulators.

What is a Quantum ML Model?
A quantum model has the ability to represent and generalize data with a quantum mechanical origin. However, to understand quantum models, two concepts must be introduced - quantum data and hybrid quantum-classical models.

Quantum data exhibits superposition and entanglement, leading to joint probability distributions that could require an exponential amount of classical computational resources to represent or store. Quantum data, which can be generated / simulated on quantum processors / sensors / networks include the simulation of chemicals and quantum matter, quantum control, quantum communication networks, quantum metrology, and much more.

A technical, but key, insight is that quantum data generated by NISQ processors are noisy and are typically entangled just before the measurement occurs. However, applying quantum machine learning to noisy entangled quantum data can maximize extraction of useful classical information. Inspired by these techniques, the TFQ library provides primitives for the development of models that disentangle and generalize correlations in quantum data, opening up opportunities to improve existing quantum algorithms or discover new quantum algorithms.

The second concept to introduce is hybrid quantum-classical models. Because near-term quantum processors are still fairly small and noisy, quantum models cannot use quantum processors alone — NISQ processors will need to work in concert with classical processors to become effective. As TensorFlow already supports heterogeneous computing across CPUs, GPUs, and TPUs, it is a natural platform for experimenting with hybrid quantum-classical algorithms.

TFQ contains the basic structures, such as qubits, gates, circuits, and measurement operators that are required for specifying quantum computations. User-specified quantum computations can then be executed in simulation or on real hardware. Cirq also contains substantial machinery that helps users design efficient algorithms for NISQ machines, such as compilers and schedulers, and enables the implementation of hybrid quantum-classical algorithms to run on quantum circuit simulators, and eventually on quantum processors.

We’ve used TensorFlow Quantum for hybrid quantum-classical convolutional neural networks, machine learning for quantum control, layer-wise learning for quantum neural networks, quantum dynamics learning, generative modeling of mixed quantum states, and learning to learn with quantum neural networks via classical recurrent neural networks. We provide a review of these quantum applications in the TFQ white paper; each example can be run in-browser via Colab from our research repository.

How TFQ works
TFQ allows researchers to construct quantum datasets, quantum models, and classical control parameters as tensors in a single computational graph. The outcome of quantum measurements, leading to classical probabilistic events, is obtained by TensorFlow Ops. Training can be done using standard Keras functions.

To provide some intuition on how to use quantum data, one may consider a supervised classification of quantum states using a quantum neural network. Just like classical ML, a key challenge of quantum ML is to classify “noisy data”. To build and train such a model, the researcher can do the following:
  1. Prepare a quantum dataset - Quantum data is loaded as tensors (a multi-dimensional array of numbers). Each quantum data tensor is specified as a quantum circuit written in Cirq that generates quantum data on the fly. The tensor is executed by TensorFlow on the quantum computer to generate a quantum dataset.
  2. Evaluate a quantum neural network model - The researcher can prototype a quantum neural network using Cirq that they will later embed inside of a TensorFlow compute graph. Parameterized quantum models can be selected from several broad categories based on knowledge of the quantum data's structure. The goal of the model is to perform quantum processing in order to extract information hidden in a typically entangled state. In other words, the quantum model essentially disentangles the input quantum data, leaving the hidden information encoded in classical correlations, thus making it accessible to local measurements and classical post-processing.
  3. Sample or Average - Measurement of quantum states extracts classical information in the form of samples from a classical random variable. The distribution of values from this random variable generally depends on the quantum state itself and on the measured observable. As many variational algorithms depend on mean values of measurements, also known as expectation values, TFQ provides methods for averaging over several runs involving steps (1) and (2).
  4. Evaluate a classical neural networks model - Once classical information has been extracted, it is in a format amenable to further classical post-processing. As the extracted information may still be encoded in classical correlations between measured expectations, classical deep neural networks can be applied to distill such correlations.
  5. Evaluate Cost Function - Given the results of classical post-processing, a cost function is evaluated. This could be based on how accurately the model performs the classification task if the quantum data was labeled, or other criteria if the task is unsupervised.
  6. Evaluate Gradients & Update Parameters - After evaluating the cost function, the free parameters in the pipeline should be updated in a direction expected to decrease the cost. This is most commonly performed via gradient descent.
A high-level abstract overview of the computational steps involved in the end-to-end pipeline for inference and training of a hybrid quantum-classical discriminative model for quantum data in TFQ. To see the code for an end-to-end example, please check the “Hello Many-Worlds” example, the quantum convolutional neural networks tutorial, and our guide.
A key feature of TensorFlow Quantum is the ability to simultaneously train and execute many quantum circuits. This is achieved by TensorFlow’s ability to parallelize computation across a cluster of computers, and the ability to simulate relatively large quantum circuits on multi-core computers. To achieve the latter, we are also announcing the release of qsim (github link), a new high performance open source quantum circuit simulator, which has demonstrated the ability to simulate a 32 qubit quantum circuit with a gate depth of 14 in 111 seconds on a single Google Cloud node (n1-ultramem-160) (see this paper for details). The simulator is particularly optimized for multi-core Intel processors. Combined with TFQ, we have demonstrated 1 million circuit simulations for 20 qubit quantum circuit at a gate depth of 20 in 60 minutes on a Google Cloud node (n2-highcpu-80). See the TFQ white paper, Section II E on the Quantum Circuit Simulation with qsim for more information.

Looking Forward
Today, TensorFlow Quantum is primarily geared towards executing quantum circuits on classical quantum circuit simulators. In the future, TFQ will be able to execute quantum circuits on actual quantum processors that are supported by Cirq, including Google’s own processor Sycamore.

To learn more about TFQ, please read our white paper and visit the TensorFlow Quantum website. We believe that bridging the ML and Quantum communities will lead to exciting new discoveries across the board and accelerate the discovery of new quantum algorithms to solve the world’s most challenging problems.

Acknowledgements
This open source project is led by the Google AI Quantum team, and was co-developed by the University of Waterloo, Alphabet’s X, and Volkswagen. A special thanks to the University of Waterloo, whose students made major contributions to this open source software through multiple internship projects at the Google AI Quantum lab.

Source: Google AI Blog


Quantum Supremacy Using a Programmable Superconducting Processor

Posted by John Martinis, Chief Scientist Quantum Hardware and Sergio Boixo, Chief Scientist Quantum Computing Theory, Google AI Quantum

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


Improving Quantum Computation with Classical Machine Learning

Posted by Murphy Yuezhen Niu and Sergio Boixo, Research Scientists 

One of the primary challenges for the realization of near-term quantum computers has to do with their most basic constituent: the qubit. Qubits can interact with anything in close proximity that carries energy close to their own—stray photons (i.e., unwanted electromagnetic fields), phonons (mechanical oscillations of the quantum device), or quantum defects (irregularities in the substrate of the chip formed during manufacturing)—which can unpredictably change the state of the qubits themselves.

Further complicating matters, there are numerous challenges posed by the tools used to control qubits. Manipulating and reading out qubits is performed via classical controls: analog signals in the form of electromagnetic fields coupled to a physical substrate in which the qubit is embedded, e.g., superconducting circuits. Imperfections in these control electronics (giving rise to white noise), interference from external sources of radiation, and fluctuations in digital-to-analog converters, introduce even more stochastic errors that degrade the performance of quantum circuits. These practical issues impact the fidelity of the computation and thus limit the applications of near-term quantum devices.

To improve the computational capacity of quantum computers, and to pave the road towards large-scale quantum computation, it is necessary to first build physical models that accurately describe these experimental problems.

In “Universal Quantum Control through Deep Reinforcement Learning”, published in Nature Partner Journal (npj) Quantum Information, we present a new quantum control framework generated using deep reinforcement learning, where various practical concerns in quantum control optimization can be encapsulated by a single control cost function. Our framework provides a reduction in the average quantum logic gate error of up to two orders-of-magnitude over standard stochastic gradient descent solutions and a significant decrease in gate time from optimal gate synthesis counterparts. Our results open a venue for wider applications in quantum simulation, quantum chemistry and quantum supremacy tests using near-term quantum devices.

The novelty of this new quantum control paradigm hinges upon the development of a quantum control function and an efficient optimization method based on deep reinforcement learning. To develop a comprehensive cost function, we first need to develop a physical model for the realistic quantum control process, one where we are able to reliably predict the amount of error. One of the most detrimental errors to the accuracy of quantum computation is leakage: the amount of quantum information lost during the computation. Such information leakage usually occurs when the quantum state of a qubit gets excited to a higher energy state, or decays to a lower energy state through spontaneous emission. Leakage errors not only lose useful quantum information, they also degrade the “quantumness” and eventually reduce the performance of a quantum computer to that of a classical one.

A common practice to accurately evaluate the leaked information during the quantum computation is to simulate the whole computation first. However, this defeats the purpose of building large-scale quantum computers, since their advantage is that they are able to perform calculations infeasible for classical systems. With improved physical modeling, our generic cost function enables a joint optimization over the accumulated leakage errors, violations of control boundary conditions, total gate time, and gate fidelity.

With the new quantum control cost function in hand, the next step is to apply an efficient optimization tool to minimize it. Existing optimization methods turn out to be unsatisfactory in finding high fidelity solutions that are also robust to control fluctuations. Instead, we apply an on-policy deep reinforcement learning (RL) method, trusted-region RL, since this method exhibits good performance in all benchmark problems, is inherently robust to sample noise, and has the capability to optimize hard control problems with hundreds of millions of control parameters. The salient difference between this on-policy RL from previously studied off-policy RL methods is that the control policy is represented independently from the control cost. Off-policy RL, such as Q-learning, on the other hand, uses a single neural network (NN) to represent both the control trajectory, and the associated reward, where the control trajectory specifies the control signals to be coupled to qubits at different time steps, and the associated award evaluates how good the current step of the quantum control is.

On-policy RL is well known for its ability to leverage non-local features in control trajectories, which becomes crucial when the control landscape is high-dimensional and packed with a combinatorially large number of non-global solutions, as is often the case for quantum systems.

We encode the control trajectory into a three-layer, fully connected NN—the policy NN—and the control cost function into a second NN—the value NN—which encodes the discounted future reward. Robust control solutions were obtained by reinforcement learning agents, which trains both NNs under a stochastic environment that mimics a realistic noisy control actuation. We provide control solutions to a set of continuously parameterized two-qubit quantum gates that are important for quantum chemistry applications but are costly to implement using the conventional universal gate set.
Under this new framework, our numerical simulations show a 100x reduction in quantum gate errors and reduced gate times for a family of continuously parameterized simulation gates by an average of one order-of-magnitude over traditional approaches using a universal gate set.

This work highlights the importance of using novel machine learning techniques and near-term quantum algorithms that leverage the flexibility and additional computational capacity of a universal quantum control scheme. More experiments are needed to integrate machine learning techniques, such as the one developed in this work, into practical quantum computation procedures to fully improve its computational capacity through machine learning.

Source: Google AI Blog


On the Path to Cryogenic Control of Quantum Processors

Posted by Joseph Bardin, Visiting Faculty Researcher and Erik Lucero, Staff Research Scientist and Hardware Lead, Google AI Quantum Team

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

Posted by Jarrod McClean, Senior Research Scientist and Hartmut Neven, Director of Engineering, Google AI Quantum Team

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

Posted by Paul V. Klimov, Research Scientist, Google AI Quantum Team

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

Cross-posted from the Google AI Blog

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!

By Alan Ho, Product Lead and Dave Bacon, Software Lead, Google AI Quantum Team

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.↩

Announcing Cirq: An Open Source Framework for NISQ Algorithms

Posted by Alan Ho, Product Lead and Dave Bacon, Software Lead, Google AI Quantum Team

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

Posted by Sergio Boixo, Research Scientist and Theory Team Lead, and Charles Neill, Quantum Electronics Engineer, Quantum A.I. Lab

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.