Tag Archives: Quantum Computing

How to compare a noisy quantum processor to a classical computer

A full-scale error-corrected quantum computer will be able to solve some problems that are impossible for classical computers, but building such a device is a huge endeavor. We are proud of the milestones that we have achieved toward a fully error-corrected quantum computer, but that large-scale computer is still some number of years away. Meanwhile, we are using our current noisy quantum processors as flexible platforms for quantum experiments.

In contrast to an error-corrected quantum computer, experiments in noisy quantum processors are currently limited to a few thousand quantum operations or gates, before noise degrades the quantum state. In 2019 we implemented a specific computational task called random circuit sampling on our quantum processor and showed for the first time that it outperformed state-of-the-art classical supercomputing.

Although they have not yet reached beyond-classical capabilities, we have also used our processors to observe novel physical phenomena, such as time crystals and Majorana edge modes, and have made new experimental discoveries, such as robust bound states of interacting photons and the noise-resilience of Majorana edge modes of Floquet evolutions.

We expect that even in this intermediate, noisy regime, we will find applications for the quantum processors in which useful quantum experiments can be performed much faster than can be calculated on classical supercomputers — we call these "computational applications" of the quantum processors. No one has yet demonstrated such a beyond-classical computational application. So as we aim to achieve this milestone, the question is: What is the best way to compare a quantum experiment run on such a quantum processor to the computational cost of a classical application?

We already know how to compare an error-corrected quantum algorithm to a classical algorithm. In that case, the field of computational complexity tells us that we can compare their respective computational costs — that is, the number of operations required to accomplish the task. But with our current experimental quantum processors, the situation is not so well defined.

In “Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments”, we provide a framework for measuring the computational cost of a quantum experiment, introducing the experiment’s “effective quantum volume”, which is the number of quantum operations or gates that contribute to a measurement outcome. We apply this framework to evaluate the computational cost of three recent experiments: our random circuit sampling experiment, our experiment measuring quantities known as “out of time order correlators” (OTOCs), and a recent experiment on a Floquet evolution related to the Ising model. We are particularly excited about OTOCs because they provide a direct way to experimentally measure the effective quantum volume of a circuit (a sequence of quantum gates or operations), which is itself a computationally difficult task for a classical computer to estimate precisely. OTOCs are also important in nuclear magnetic resonance and electron spin resonance spectroscopy. Therefore, we believe that OTOC experiments are a promising candidate for a first-ever computational application of quantum processors.

Plot of computational cost and impact of some recent quantum experiments. While some (e.g., QC-QMC 2022) have had high impact and others (e.g., RCS 2023) have had high computational cost, none have yet been both useful and hard enough to be considered a “computational application.” We hypothesize that our future OTOC experiment could be the first to pass this threshold. Other experiments plotted are referenced in the text.

Random circuit sampling: Evaluating the computational cost of a noisy circuit

When it comes to running a quantum circuit on a noisy quantum processor, there are two competing considerations. On one hand, we aim to do something that is difficult to achieve classically. The computational cost — the number of operations required to accomplish the task on a classical computer — depends on the quantum circuit’s effective quantum volume: the larger the volume, the higher the computational cost, and the more a quantum processor can outperform a classical one.

But on the other hand, on a noisy processor, each quantum gate can introduce an error to the calculation. The more operations, the higher the error, and the lower the fidelity of the quantum circuit in measuring a quantity of interest. Under this consideration, we might prefer simpler circuits with a smaller effective volume, but these are easily simulated by classical computers. The balance of these competing considerations, which we want to maximize, is called the "computational resource", shown below.

Graph of the tradeoff between quantum volume and noise in a quantum circuit, captured in a quantity called the “computational resource.” For a noisy quantum circuit, this will initially increase with the computational cost, but eventually, noise will overrun the circuit and cause it to decrease.

We can see how these competing considerations play out in a simple “hello world” program for quantum processors, known as random circuit sampling (RCS), which was the first demonstration of a quantum processor outperforming a classical computer. Any error in any gate is likely to make this experiment fail. Inevitably, this is a hard experiment to achieve with significant fidelity, and thus it also serves as a benchmark of system fidelity. But it also corresponds to the highest known computational cost achievable by a quantum processor. We recently reported the most powerful RCS experiment performed to date, with a low measured experimental fidelity of 1.7x10-3, and a high theoretical computational cost of ~1023. These quantum circuits had 700 two-qubit gates. We estimate that this experiment would take ~47 years to simulate in the world's largest supercomputer. While this checks one of the two boxes needed for a computational application — it outperforms a classical supercomputer — it is not a particularly useful application per se.

OTOCs and Floquet evolution: The effective quantum volume of a local observable

There are many open questions in quantum many-body physics that are classically intractable, so running some of these experiments on our quantum processor has great potential. We typically think of these experiments a bit differently than we do the RCS experiment. Rather than measuring the quantum state of all qubits at the end of the experiment, we are usually concerned with more specific, local physical observables. Because not every operation in the circuit necessarily impacts the observable, a local observable’s effective quantum volume might be smaller than that of the full circuit needed to run the experiment.

We can understand this by applying the concept of a light cone from relativity, which determines which events in space-time can be causally connected: some events cannot possibly influence one another because information takes time to propagate between them. We say that two such events are outside their respective light cones. In a quantum experiment, we replace the light cone with something called a “butterfly cone,” where the growth of the cone is determined by the butterfly speed — the speed with which information spreads throughout the system. (This speed is characterized by measuring OTOCs, discussed later.) The effective quantum volume of a local observable is essentially the volume of the butterfly cone, including only the quantum operations that are causally connected to the observable. So, the faster information spreads in a system, the larger the effective volume and therefore the harder it is to simulate classically.

A depiction of the effective volume Veff of the gates contributing to the local observable B. A related quantity called the effective area Aeff is represented by the cross-section of the plane and the cone. The perimeter of the base corresponds to the front of information travel that moves with the butterfly velocity vB.

We apply this framework to a recent experiment implementing a so-called Floquet Ising model, a physical model related to the time crystal and Majorana experiments. From the data of this experiment, one can directly estimate an effective fidelity of 0.37 for the largest circuits. With the measured gate error rate of ~1%, this gives an estimated effective volume of ~100. This is much smaller than the light cone, which included two thousand gates on 127 qubits. So, the butterfly velocity of this experiment is quite small. Indeed, we argue that the effective volume covers only ~28 qubits, not 127, using numerical simulations that obtain a larger precision than the experiment. This small effective volume has also been corroborated with the OTOC technique. Although this was a deep circuit, the estimated computational cost is 5x1011, almost one trillion times less than the recent RCS experiment. Correspondingly, this experiment can be simulated in less than a second per data point on a single A100 GPU. So, while this is certainly a useful application, it does not fulfill the second requirement of a computational application: substantially outperforming a classical simulation.

Information scrambling experiments with OTOCs are a promising avenue for a computational application. OTOCs can tell us important physical information about a system, such as the butterfly velocity, which is critical for precisely measuring the effective quantum volume of a circuit. OTOC experiments with fast entangling gates offer a potential path for a first beyond-classical demonstration of a computational application with a quantum processor. Indeed, in our experiment from 2021 we achieved an effective fidelity of Feff ~ 0.06 with an experimental signal-to-noise ratio of ~1, corresponding to an effective volume of ~250 gates and a computational cost of 2x1012.

While these early OTOC experiments are not sufficiently complex to outperform classical simulations, there is a deep physical reason why OTOC experiments are good candidates for the first demonstration of a computational application. Most of the interesting quantum phenomena accessible to near-term quantum processors that are hard to simulate classically correspond to a quantum circuit exploring many, many quantum energy levels. Such evolutions are typically chaotic and standard time-order correlators (TOC) decay very quickly to a purely random average in this regime. There is no experimental signal left. This does not happen for OTOC measurements, which allows us to grow complexity at will, only limited by the error per gate. We anticipate that a reduction of the error rate by half would double the computational cost, pushing this experiment to the beyond-classical regime.


Using the effective quantum volume framework we have developed, we have determined the computational cost of our RCS and OTOC experiments, as well as a recent Floquet evolution experiment. While none of these meet the requirements yet for a computational application, we expect that with improved error rates, an OTOC experiment will be the first beyond-classical, useful application of a quantum processor.

Source: Google AI Blog

The world’s first braiding of non-Abelian anyons

Imagine you’re shown two identical objects and then asked to close your eyes. When you open your eyes, you see the same two objects in the same position. How can you determine if they have been swapped back and forth? Intuition and the laws of quantum mechanics agree: If the objects are truly identical, there is no way to tell.

While this sounds like common sense, it only applies to our familiar three-dimensional world. Researchers have predicted that for a special type of particle, called an anyon, that is restricted to move only in a two-dimensional (2D) plane, quantum mechanics allows for something quite different. Anyons are indistinguishable from one another and some, non-Abelian anyons, have a special property that causes observable differences in the shared quantum state under exchange, making it possible to tell when they have been exchanged, despite being fully indistinguishable from one another. While researchers have managed to detect their relatives, Abelian anyons, whose change under exchange is more subtle and impossible to directly detect, realizing “non-Abelian exchange behavior” has proven more difficult due to challenges with both control and detection.

In “Non-Abelian braiding of graph vertices in a superconducting processor”, published in Nature, we report the observation of this non-Abelian exchange behavior for the first time. Non-Abelian anyons could open a new avenue for quantum computation, in which quantum operations are achieved by swapping particles around one another like strings are swapped around one another to create braids. Realizing this new exchange behavior on our superconducting quantum processor could be an alternate route to so-called topological quantum computation, which benefits from being robust against environmental noise.

Exchange statistics and non-Abelian anyons

In order to understand how this strange non-Abelian behavior can occur, it’s helpful to consider an analogy with the braiding of two strings. Take two identical strings and lay them parallel next to one another. Swap their ends to form a double-helix shape. The strings are identical, but because they wrap around one another when the ends are exchanged, it is very clear when the two ends are swapped.

The exchange of non-Abelian anyons can be visualized in a similar way, where the strings are made from extending the particles’ positions into the time dimension to form “world-lines.” Imagine plotting two particles’ locations vs. time. If the particles stay put, the plot would simply be two parallel lines, representing their constant locations. But if we exchange the locations of the particles, the world lines wrap around one another. Exchange them a second time, and you’ve made a knot.

While a bit difficult to visualize, knots in four dimensions (three spatial plus one time dimension) can always easily be undone. They are trivial — like a shoelace, simply pull one end and it unravels. But when the particles are restricted to two spatial dimensions, the knots are in three total dimensions and — as we know from our everyday 3D lives — cannot always be easily untied. The braiding of the non-Abelian anyons’ world lines can be used as quantum computing operations to transform the state of the particles.

A key aspect of non-Abelian anyons is “degeneracy”: the full state of several separated anyons is not completely specified by local information, allowing the same anyon configuration to represent superpositions of several quantum states. Winding non-Abelian anyons about each other can change the encoded state.

How to make a non-Abelian anyon

So how do we realize non-Abelian braiding with one of Google’s quantum processors? We start with the familiar surface code, which we recently used to achieve a milestone in quantum error correction, where qubits are arranged on the vertices of a checkerboard pattern. Each color square of the checkerboard represents one of two possible joint measurements that can be made of the qubits on the four corners of the square. These so-called “stabilizer measurements” can return a value of either + or – 1. The latter is referred to as a plaquette violation, and can be created and moved diagonally — just like bishops in chess — by applying single-qubit X- and Z-gates. Recently, we showed that these bishop-like plaquette violations are Abelian anyons. In contrast to non-Abelian anyons, the state of Abelian anyons changes only subtly when they are swapped — so subtly that it is impossible to directly detect. While Abelian anyons are interesting, they do not hold the same promise for topological quantum computing that non-Abelian anyons do.

To produce non-Abelian anyons, we need to control the degeneracy (i.e., the number of wavefunctions that causes all stabilizer measurements to be +1). Since a stabilizer measurement returns two possible values, each stabilizer cuts the degeneracy of the system in half, and with sufficiently many stabilizers, only one wave function satisfies the criterion. Hence, a simple way to increase the degeneracy is to merge two stabilizers together. In the process of doing so, we remove one edge in the stabilizer grid, giving rise to two points where only three edges intersect. These points, referred to as “degree-3 vertices” (D3Vs), are predicted to be non-Abelian anyons.

In order to braid the D3Vs, we have to move them, meaning that we have to stretch and squash the stabilizers into new shapes. We accomplish this by implementing two-qubit gates between the anyons and their neighbors (middle and right panels shown below).

Non-Abelian anyons in stabilizer codes. a: Example of a knot made by braiding two anyons’ world lines. b: Single-qubit gates can be used to create and move stabilizers with a value of –1 (red squares). Like bishops in chess, these can only move diagonally and are therefore constrained to one sublattice in the regular surface code. This constraint is broken when D3Vs (yellow triangles) are introduced. c: Process to form and move D3Vs (predicted to be non-Abelian anyons). We start with the surface code, where each square corresponds to a joint measurement of the four qubits on its corners (left panel). We remove an edge separating two neighboring squares, such that there is now a single joint measurement of all six qubits (middle panel). This creates two D3Vs, which are non-Abelian anyons. We move the D3Vs by applying two-qubit gates between neighboring sites (right panel).

Now that we have a way to create and move the non-Abelian anyons, we need to verify their anyonic behavior. For this we examine three characteristics that would be expected of non-Abelian anyons:

  1. The “fusion rules” — What happens when non-Abelian anyons collide with each other?
  2. Exchange statistics — What happens when they are braided around one another?
  3. Topological quantum computing primitives — Can we encode qubits in the non-Abelian anyons and use braiding to perform two-qubit entangling operations?

The fusion rules of non-Abelian anyons

We investigate fusion rules by studying how a pair of D3Vs interact with the bishop-like plaquette violations introduced above. In particular, we create a pair of these and bring one of them around a D3V by applying single-qubit gates.

While the rules of bishops in chess dictate that the plaquette violations can never meet, the dislocation in the checkerboard lattice allows them to break this rule, meet its partner and annihilate with it. The plaquette violations have now disappeared! But bring the non-Abelian anyons back in contact with one another, and the anyons suddenly morph into the missing plaquette violations. As weird as this behavior seems, it is a manifestation of exactly the fusion rules that we expect these entities to obey. This establishes confidence that the D3Vs are, indeed, non-Abelian anyons.

Demonstration of anyonic fusion rules (starting with panel I, in the lower left). We form and separate two D3Vs (yellow triangles), then form two adjacent plaquette violations (red squares) and pass one between the D3Vs. The D3Vs deformation of the “chessboard” changes the bishop rules of the plaquette violations. While they used to lie on adjacent squares, they are now able to move along the same diagonals and collide (as shown by the red lines). When they do collide, they annihilate one another. The D3Vs are brought back together and surprisingly morph into the missing adjacent red plaquette violations.

Observation of non-Abelian exchange statistics

After establishing the fusion rules, we want to see the real smoking gun of non-Abelian anyons: non-Abelian exchange statistics. We create two pairs of non-Abelian anyons, then braid them by wrapping one from each pair around each other (shown below). When we fuse the two pairs back together, two pairs of plaquette violations appear. The simple act of braiding the anyons around one another changed the observables of our system. In other words, if you closed your eyes while the non-Abelian anyons were being exchanged, you would still be able to tell that they had been exchanged once you opened your eyes. This is the hallmark of non-Abelian statistics.

Braiding non-Abelian anyons. We make two pairs of D3Vs (panel II), then bring one from each pair around each other (III-XI). When fusing the two pairs together again in panel XII, two pairs of plaquette violations appear! Braiding the non-Abelian anyons changed the observables of the system from panel I to panel XII; a direct manifestation of non-Abelian exchange statistics.

Topological quantum computing

Finally, after establishing their fusion rules and exchange statistics, we demonstrate how we can use these particles in quantum computations. The non-Abelian anyons can be used to encode information, represented by logical qubits, which should be distinguished from the actual physical qubits used in the experiment. The number of logical qubits encoded in N D3Vs can be shown to be N/2–1, so we use N=8 D3Vs to encode three logical qubits, and perform braiding to entangle them. By studying the resulting state, we find that the braiding has indeed led to the formation of the desired, well-known quantum entangled state called the Greenberger-Horne-Zeilinger (GHZ) state.

Using non-Abelian anyons as logical qubits. a, We braid the non-Abelian anyons to entangle three qubits encoded in eight D3Vs. b, Quantum state tomography allows for reconstructing the density matrix, which can be represented in a 3D bar plot and is found to be consistent with the desired highly entangled GHZ-state.


Our experiments show the first observation of non-Abelian exchange statistics, and that braiding of the D3Vs can be used to perform quantum computations. With future additions, including error correction during the braiding procedure, this could be a major step towards topological quantum computation, a long-sought method to endow qubits with intrinsic resilience against fluctuations and noise that would otherwise cause errors in computations.


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

Source: Google AI Blog

Suppressing quantum errors by scaling a surface code logical qubit

Many years from today, scientists will be able to use fault-tolerant quantum computers for large-scale computations with applications across science and industry. These quantum computers will be much bigger than today, consisting of millions of coherent quantum bits, or qubits. But there’s a catch — these basic building blocks must be good enough or the systems will be overrun with errors.

Currently, the error rates of the qubits on our 3rd generation Sycamore processor are typically between 1 in 10,000 to 1 in 100. Through our work and that of others, we understand that developing large-scale quantum computers will require far lower error rates. We will need rates in the range of 1 in 109 to 1 in 106 to run quantum circuits that can solve industrially relevant problems.

So how do we get there, knowing that squeezing three to six orders of magnitude of better performance from our current physical qubits is unlikely? Our team has created a roadmap that has directed our research for the last several years, improving the performance of our quantum computers in gradual steps toward a fault-tolerant quantum computer.

Roadmap for building a useful error-corrected quantum computer with key milestones. We are currently building one logical qubit that we will scale in the future.

Today, in “Suppressing Quantum Errors by Scaling a Surface Code Logical Qubit”, published in Nature, we are announcing that we have reached the second milestone on our roadmap. Our experimental results demonstrate a prototype of the basic unit of an error-corrected quantum computer known as a logical qubit, with performance nearing the regime that enables scalable fault-tolerant quantum computing.

From physical qubits to logical qubits

Quantum error correction (QEC) represents a significant shift from today’s quantum computing, where each physical qubit on the processor acts as a unit of computation. It provides the recipe to reach low errors by trading many good qubits for an excellent one: information is encoded across several physical qubits to construct a single logical qubit that is more resilient and capable of running large-scale quantum algorithms. Under the right conditions, the more physical qubits used to build a logical qubit, the better that logical qubit becomes.

However, this will not work if the added errors from each additional physical qubit outweigh the benefits of QEC. Until now, the high physical error rates have always won out.

To that end, we use a particular error-correcting code called a surface code and show for the first time that increasing the size of the code decreases the error rate of the logical qubit. A first-ever for any quantum computing platform, this was achieved by painstakingly mitigating many error sources as we scaled from 17 to 49 physical qubits. This work is evidence that with enough care, we can produce the logical qubits necessary for a large-scale error-corrected quantum computer.

Quantum error correction with surface codes

How does an error-correcting code protect information? Take a simple example from classical communication: Bob wants to send Alice a single bit that reads “1” across a noisy communication channel. Recognizing that the message is lost if the bit flips to “0”, Bob instead sends three bits: “111”. If one erroneously flips, Alice could take a majority vote (a simple error-correcting code) of all the received bits and still understand the intended message. Repeating the information more than three times — increasing the “size” of the code — would enable the code to tolerate more individual errors.

Many physical qubits on a quantum processor acting as one logical qubit in an error-correcting code called a surface code.

A surface code takes this principle and imagines a practical quantum implementation. It has to satisfy two additional constraints. First, the surface code must be able to correct not just bit flips, taking a qubit from |0 to |1, but also phase flips. This error is unique to quantum states and transforms a qubit in a superposition state, for example from “|0 + |1” to “|0 - |1”. Second, checking the qubits’ states would destroy their superpositions, so one needs a way of detecting errors without measuring the states directly.

To address these constraints, we arrange two types of qubits on a checkerboard. “Data” qubits on the vertices make up the logical qubit, while “measure” qubits at the center of each square are used for so-called “stabilizer measurements.” These measurements tell us whether the qubits are all the same, as desired, or different, signaling that an error occurred, without actually revealing the value of the individual data qubits.

We tile two types of stabilizer measurements in a checkerboard pattern to protect the logical data from bit- and phase-flips. If some of the stabilizer measurements register an error, then correlations in the stabilizer measurements are used to identify which error(s) occurred and where.

Surface-code QEC. Data qubits (yellow) are at the vertices of a checkerboard. Measure qubits at the center of each square are used for stabilizer measurements (blue squares). Dark blue squares check for bit-flip errors, while light blue squares check for phase-flip errors. Left: A phase-flip error. The two nearest light blue stabilizer measurements register the error (light red). Right: A bit-flip error. The two nearest dark blue stabilizer measurements register the error (dark red).

Just as Bob’s message to Alice in the example above became more robust against errors with increasing code size, a larger surface code better protects the logical information it contains. The surface code can withstand a number of bit- and phase-flip errors each equal to less than half the distance, where the distance is the number of data qubits that span the surface code in either dimension.

But here’s the problem: every individual physical qubit is prone to errors, so the more qubits in a code, the more opportunity for errors. We want the higher protection offered by QEC to outweigh the increased opportunities for errors as we increase the number of qubits. For this to happen, the physical qubits must have errors below the so-called “fault-tolerant threshold.” For the surface code, this threshold is quite low. So low that it hasn’t been experimentally feasible until recently. We are now on the precipice of reaching this coveted regime.

Making and controlling high-quality physical qubits

Entering the regime where QEC improves with scale required improving every aspect of our quantum computers, from nanofabrication of the physical qubits to the optimized control of the full quantum system. These experiments ran on a state-of-the-art 3rd generation Sycamore processor architecture optimized for QEC using the surface code with improvements across the board:

  • Increased qubit relaxation and dephasing lifetimes through an improved fabrication process and environmental noise reduction near the quantum processor.
  • Lowered cross-talk between all physical qubits during parallel operation by optimizing quantum processor circuit design and nanofabrication.
  • Reduced drift and improved qubit control fidelity through upgraded custom electronics.
  • Implemented faster and higher-fidelity readout and reset operations compared with previous generations of the Sycamore processor.
  • Reduced calibration errors by extensively modeling the full quantum system and employing better system-optimization algorithms.
  • Developed context-aware and fully parallel calibrations to minimize drift and optimize control parameters for QEC circuits.
  • Enhanced dynamical decoupling protocols to protect physical qubits from noise and cross-talk during idling operations.

Running surface code circuits

With these upgrades in place, we ran experiments to compare the ratio (𝚲3,5) between the logical error rate of a distance-3 surface code (ε3) with 17 qubits to that of a distance-5 surface code (ε5) with 49 qubits — 𝚲3,5 = ε3 / ε5.

Comparison of logical fidelity (defined as 1-ε) between distance-3 (d=3) and distance-5 (d=5) surface codes. The distance-5 code contains four possible distance-3 arrangements, with one example shown in the red outline (left). As improvements were made, the d=5 fidelity increased faster than that of the d=3, eventually overtaking the distance-3 code, as shown in the top-right data points (right), whose average lies slightly to the left of the ε3 = ε5 line.

The results of these experiments are shown above on the right. Continued improvements over several months allowed us to reduce the logical errors of both grids, leading to the distance-5 grid (ε5 = 2.914%) outperforming the distance-3 grids (ε3 = 3.028%) by 4% (𝚲3,5 = 1.04) with 5𝛔 confidence. While this might seem like a small improvement, it’s important to emphasize that the result represents a first for the field since Peter Shor’s 1995 QEC proposal. A larger code outperforming a smaller one is a key signature of QEC, and all quantum computing architectures will need to pass this hurdle to realize a path to the low errors that are necessary for quantum applications.

The path forward

These results indicate that we are entering a new era of practical QEC. The Google Quantum AI team has spent the last few years thinking about how we define success in this new era, and how we measure progress along the way.

The ultimate goal is to demonstrate a pathway to achieving the low errors needed for using quantum computers in meaningful applications. To this end, our target remains achieving logical error rates of 1 in 106 or lower per cycle of QEC. In the figure below on the left, we outline the path that we anticipate to reach this target. As we continue improving our physical qubits (and hence the performance of our logical qubits), we expect to gradually increase 𝚲 from close to 1 in this work to larger numbers. The figure below shows that a value of 𝚲 = 4 and a code distance of 17 (577 physical qubits with good enough quality) will yield a logical error rate below our target of 1 in 106.

While this result is still a few years out, we have an experimental technique to probe error rates this low with today’s hardware, albeit in limited circumstances. While two-dimensional surface codes allow us to correct both bit- and phase-flip errors, we can also construct one-dimensional repetition codes that are only able to solve one type of error with relaxed requirements. On the right below, we show that a distance-25 repetition code can reach error rates per cycle close to 1 in 106. At such low errors, we see new kinds of error mechanisms that are not yet observable with our surface codes. By controlling for these error mechanisms, we can improve repetition codes to error rates near 1 in 107.

Left: Expected progression as we improve performance (quantified by 𝚲) and scale (quantified by code distance) for surface codes. Right: Experimentally measured logical error rates per cycle versus the distance of one-dimensional repetition codes and two-dimensional surface codes.

Reaching this milestone reflects three years of focused work by the entire Google Quantum AI team following our demonstration of a quantum computer outperforming a classical computer. In our march toward building fault-tolerant quantum computers, we will continue to use the target error rates in the figure above to measure our progress. With further improvements toward our next milestone, we anticipate entering the fault-tolerant regime, where we can exponentially suppress logical errors and unlock the first useful error-corrected quantum applications. In the meantime, we continue to explore various ways of solving problems using quantum computers in topics ranging from condensed matter physics to chemistry, machine learning, and materials science.

Source: Google AI Blog

Google Research, 2022 & beyond: Natural sciences

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

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

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

Using machine learning to unlock mysteries in biology

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


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

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

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

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


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

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

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

Using quantum computing for new physics discoveries

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

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

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

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

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


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


Google Research, 2022 & beyond

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

Source: Google AI Blog

Amplification at the Quantum limit

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

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

Why microwave amplifiers?

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

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

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

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


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

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

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

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

Conclusion and future directions

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


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

Source: Google AI Blog

Formation of Robust Bound States of Interacting Photons

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

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

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


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

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

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

Bound Photons

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

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

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

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

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

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

Bound States Behave Like Single Composite Particles

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

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

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

Breaking Integrability

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

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

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

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


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


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

Source: Google AI Blog

Making a Traversable Wormhole with a Quantum Computer

Wormholes — wrinkles in the fabric of spacetime that connect two disparate locations — may seem like the stuff of science fiction. But whether or not they exist in reality, studying these hypothetical objects could be the key to making concrete the tantalizing link between information and matter that has bedeviled physicists for decades.

Surprisingly, a quantum computer is an ideal platform to investigate this connection. The trick is to use a correspondence called AdS/CFT, which establishes an equivalence between a theory that describes gravity and spacetime (and wormholes) in a fictional world with a special geometry (AdS) to a quantum theory that does not contain gravity at all (CFT).

In “Traversable wormhole dynamics on a quantum processor”, published in Nature today, we report on a collaboration with researchers at Caltech, Harvard, MIT, and Fermilab to simulate the CFT on the Google Sycamore processor. By studying this quantum theory on the processor, we are able to leverage the AdS/CFT correspondence to probe the dynamics of a quantum system equivalent to a wormhole in a model of gravity. The Google Sycamore processor is among the first to have the fidelity needed to carry out this experiment.

Background: It from Qubit

The AdS/CFT correspondence was discovered at the end of a series of inquiries arising from the question: What’s the maximum amount of information that can fit in a single region of space? If one asked an engineer how much information could possibly be stored in a datacenter the answer would likely be that it depends on the number and type of memory chips inside it. But surprisingly, what is inside the data center is ultimately irrelevant. If one were to cram more and more memory chips with denser and denser electronics into the datacenter then it will eventually collapse into a black hole and disappear behind an event horizon.

When physicists such as Jacob Bekenstein and Stephen Hawking tried to compute the information content of a black hole, they found to their surprise that it is given by the area of the event horizon — not by the volume of the black hole. It looks as if the information inside the black hole was written on the event horizon. Specifically, a black hole with an event horizon that can be tiled with A tiny units of area (each unit, called a “Planck area,” is 2.6121×10−70 m2) has at most A/4 bits of information. This limit is known as the Bekenstein-Hawking bound.

This discovery that the maximum amount of information that could fit in a region was proportional not to its volume, but to the surface area of the region’s boundary hinted at an intriguing relationship between quantum information and the three-dimensional spatial world of our everyday experience. This relationship has been epitomized by the phrase “It from qubit,” describing how matter (“it”) emerges from quantum information (“qubit”).

While formalizing such a relationship is difficult for ordinary spacetime, recent research has led to remarkable progress with a hypothetical universe with hyperbolic geometry known as “anti-de Sitter space” in which the theory of quantum gravity is more naturally constructed. In anti-de Sitter space, the description of a volume of space with gravity acting in it can be thought of as encoded on the boundary enclosing the volume: every object inside the space has a corresponding description on the boundary and vice versa. This correspondence of information is called the holographic principle, which is a general principle inspired by Bekenstein and Hawking's observations.

Schematic representation of anti-de Sitter space (interior of cylinder) and its dual representation as quantum information on the boundary (surface of cylinder).

The AdS/CFT correspondence allows physicists to connect objects in space with specific ensembles of interacting qubits on the surface. That is, each region of the boundary encodes (in quantum information) the content of a region in spacetime such that matter at any given location can be "constructed" from the quantum information. This allows quantum processors to work directly with qubits while providing insights into spacetime physics. By carefully defining the parameters of the quantum computer to emulate a given model, we can look at black holes, or even go further and look at two black holes connected to each other — a configuration known as a wormhole, or an Einstein-Rosen bridge.

Experiment: Quantum Gravity in the Lab

Implementing these ideas on a Sycamore processor, we have constructed a quantum system that is dual to a traversable wormhole. Translated from the language of quantum information to spacetime physics via the holographic principle, the experiment let a particle fall into one side of a wormhole and observed it emerging on the other side.

Traversable wormholes were recently shown to be possible by Daniel Jafferis, Ping Gao and Aron Wall. While wormholes have long been a staple of science fiction, there are many possible spacetime geometries in which the formation of a wormhole is possible, but a naïvely constructed one would collapse on a particle traveling through it. The authors showed that a shockwave — i.e., a deformation of spacetime that propagates at the speed of light — of negative energy would solve this problem, propping open the wormhole long enough to enable traversability. The presence of negative energy in a traversable wormhole is similar to negative energy in the Casimir effect, where vacuum energy pushes together closely spaced plates. In both cases, quantum mechanics permits the energy density at a given location in space to be either positive or negative. On the other hand, if the wormhole experienced a shockwave of positive energy, no information would be allowed to pass through.

The simplest application of the holographic principle to create a wormhole requires many, many qubits — in fact, to approach the pencil-and-paper solutions given by theoretical physicists, one would need an arbitrarily large number of qubits. As the number of qubits is reduced, additional corrections are required that are still poorly understood today. New ideas were needed to build a traversable wormhole on a quantum computer with a limited number of qubits.

One of us (Zlokapa) adopted ideas from deep learning to design a small quantum system that preserved key aspects of gravitational physics. Neural networks are trained via backpropagation, a method that optimizes parameters by directly computing the gradient through the layers of the network. To improve the performance of a neural network and prevent it from overfitting to the training dataset, machine learning (ML) practitioners employ a host of techniques. One of these, sparsification, attempts to restrict the detail of information in the network by setting as many weights as possible to zero.

Similarly, to create the wormhole, we started with a large quantum system and treated it like a neural network. Backpropagation updated the parameters of the system in order to maintain gravitational properties while sparsification reduced the size of the system. We applied ML to learn a system that preserved only one key gravitational signature: the importance of using a negative energy shockwave. The training dataset compared dynamics of a particle traversing a wormhole propped open with negative energy and collapsed with positive energy. By ensuring the learned system preserved this asymmetry, we obtained a sparse model consistent with wormhole dynamics.

Learning procedure to produce a sparse quantum system that captures gravitational dynamics. A single coupling consists of all six possible connections between a given group of four fermions.

Working with Jafferis and a handful of collaborators from Caltech, Fermilab, and Harvard, we subjected the new quantum system to numerous tests to determine if it showed gravitational behavior beyond signatures induced by different energy shockwaves. For example, while quantum mechanical effects can transmit information across a quantum system in a diverse set of ways, information that travels in spacetime — including through a wormhole — must be causally consistent. This and other signatures were verified on classical computers, confirming that the dynamics of the quantum system were consistent with a gravitational interpretation as viewed through the dictionary of the holographic principle.

Implementing the traversable wormhole as an experiment on a quantum processor is an extraordinarily delicate process. The microscopic mechanism of information transfer across qubits is highly chaotic: imagine an ink drop swirling in water. As a particle falls into a wormhole, its information gets smeared over the entire quantum system in the holographic picture. For the negative energy shockwave to work, the scrambling of information must follow a particular pattern known as perfect size winding. After the particle hits the negative energy shockwave, the chaotic patterns effectively proceed in reverse: when the particle emerges from the wormhole, it is as if the ink drop has come back together by exactly undoing its original turbulent spread. If, at any point in time, a small error occurs, the chaotic dynamics will not undo themselves, and the particle will not make it through the wormhole.

Left: Quantum circuit describing a traversable wormhole. A maximally entangled pair of qubits (“EPR pair”) are used as an entanglement probe to send a qubit through the wormhole. The qubit is swapped into the left side of the wormhole at time –t0; the energy shockwave is applied at time 0; and the right side of the wormhole is measured at time t1. Right: Photograph of the Google Sycamore quantum processor.

On the Sycamore quantum processor, we measured how much quantum information passed from one side of the system to the other when applying a negative versus a positive energy shockwave. We observed a slight asymmetry between the two energies, showing the key signature of a traversable wormhole. Due to the protocol’s sensitivity to noise, the Sycamore processor’s low error rates were critical to measuring the signal; with even 1.5x the amount of noise, the signal would have been entirely obscured.

Looking Forward

As quantum devices continue to improve, lower error rates and larger chips will allow deeper probes of gravitational phenomena. Unlike experiments such as LIGO that record data about gravity in the world around us, quantum computers provide a tool to explore theories of quantum gravity. We hope that quantum computers will help develop our understanding of future theories of quantum gravity beyond current models.

Gravity is only one example of the unique ability of quantum computers to probe complex physical theories: quantum processors can provide insight into time crystals, quantum chaos, and chemistry. Our work demonstrating wormhole dynamics represents a step towards discovering fundamental physics using quantum processors at Google Quantum AI.

You can also read more about this result here.


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

Source: Google AI Blog

Cirq Turns 1.0

Today we are excited to announce the first full version release of the open source quantum programming framework Cirq: Cirq 1.0. Cirq is a Python framework for writing, running, and analyzing the results of quantum computer programs. It was designed for near-term quantum computers, those with a few hundred qubits and few thousands of quantum gates. The significance of the 1.0 release is that Cirq has support for the vast majority of workflows for these systems and is considered to be a stable API that we will only update with breaking changes at major version numbers.

Getting to Cirq 1.0 is the culmination of a large amount of hard work by hundreds of contributors from Google, industry, and academia. We have been running a weekly meeting, called the “Cirq Cync”, for over four years where community members gather to discuss work on Cirq, bugs, and to generally tell terrible but amusing quantum programming jokes. We’re proud of this inclusive community, and we’ve been particularly happy to see the growth of many software developers into quantum computing experts, and quantum computing experts into solid software developers. One of our contributors, Victory Omole, won the 2021 Witteck Quantum Prize for Open Source Software. Way to go Victory!

The first commit to Cirq on GitHub (an internal version of Cirq at Google existed prior to this) was on Dec 19, 2017 by Craig Gidney, and we publicly announced Cirq in July of 2018. 3,200+ commits later to the GitHub repo, in the hands of the team at Google and the Cirq community, we’ve seen Cirq help accomplish some amazing things:
  • Cirq is the lingua franca that Google’s hardware team uses to write quantum programs that run on Google’s quantum computing hardware. Because of this, we have been able to post open source code in our ReCirq repo for these experiments for anyone to examine and extend. A few highlights of the past few years:
    • “Realizing topologically ordered states on a quantum processor”, K. J. Satzinger et al., Science 374 6572, 1237-1241 (2021) [paper] [ReCirq code]
    • “Information scrambling in quantum circuits”, X. Mi, P. Roushan, C. Quintana et al, Science 374, 6574 1479-1483 (2021) [paper] [ReCirq code]
    • “Hartree-Fock on a superconducting qubit quantum computer”, F. Arute et al., Science 369, 6507 1084--1089 (2020) [paper] [ReCirq code]
  • A healthy community of libraries have now been built on top of Cirq, enabling different quantum computing research areas. These libraries include:
    • TensorFlow Quantum: a tool for exploring quantum machine learning. Using TensorFlow Quantum researchers trained a machine learning model on 30 qubits at a rate of 1.1 petaflops per second (1.1 x 1015 operations per second).
    • OpenFermion: an open source tool for quantum computations involved in chemistry simulations.
    • Pytket (pytkey-cirq): an open source Python tool for optimizing and manipulating quantum circuits.
    • Mitiq: an open source library developed by the non-profit Unitary fund for error mitigation techniques developed by the non-profit Unitary fund.
    • Qsim: a high performance state vector simulator written using AVX/FMA vectorized instructions with optional GPU acceleration. qsimcirq is the Cirq interface one can use to access qsim from Cirq.
  • Numerous quantum computing cloud services from companies in the industry have also integrated/standardized Cirq. Programs written in Cirq can be used to run through AQT, IonQ, Pascal, Rigetti, and IQM vendors. In addition, Cirq can be used on Azure Quantum to run on the hardware supported by Azure Quantum. Finally, one can get realistic noise simulations of Google’s quantum computing hardware using our newly released Quantum Virtual Machine.
  • Cirq is not just for stuffy research. Cirq has also been used to help develop Quantum Chess, a version of chess that uses superposition and entanglement. This notebook shows you how the game of Quantum Chess can be programmed using Cirq.
Cirq moving to its first full version does not just come with new features (see 1.0 release notes), but also with more guarantees about stability. Cirq uses semantic versioning, which means that future point release of Cirq will be compatible with the full version release. For example, version 1.1 of Cirq will not introduce breaking changes to Cirq’s interfaces from version 1.0; only at major version bumps (from 1.x to 2.0, for example) will breaking changes occur.

When we began working on Cirq, quantum computers consisted of only a few qubits and a few quantum gates on these qubits. Building Cirq and the supporting software for these custom systems and having them start to scale to hundreds of qubits over the past (nearly) five years has taught us many lessons. One key takeaway from these lessons is that: As quantum computing hardware continues to grow in scale and complexity, we expect that making software to support this growth will be essential to continue meaningful research and progress. In the next five years, with hardware expected to reach hundreds or even thousands of qubits, the software that is developed for quantum computing will need to have a careful eye set on supporting these bigger and bigger systems. Going forward we will need an ever wider set of frameworks, programming languages, and libraries to achieve quantum computing’s promise.


We are indebted to all 169 contributors to the Cirq github repo, and the many more who have filed issues and used Cirq in their own software. A particular shout out to the original lead of Cirq, Craig Gidney, to Cirq’s second lead, ‪Bálint Pató who guided Cirq through its middle ages, and to Alan Ho and Catherine Vollgraff Heidweiller for product wisdom. A special thanks to the core Cirq contributors including Doug Strain, Matthew Neely, Tanuj Khatter, Dax Fohl, Adam Zalcman, Kevin Sung, Matt Harrigan, Casey Duckering, Orion Martin, Smit Sanghavi, Bryan O'Gorman, Wojciech Mruczkiewicz, Ryan LaRose, Tony Bruguier, Victory Omole, and Cheng Xing, and our documentarians Auguste Hirth and Abe Asfaw.

By Dave Bacon and Michael Broughton – Quantum AI Team

Quantum Advantage in Learning from Experiments

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Source: Google AI Blog

Hybrid Quantum Algorithms for Quantum Monte Carlo

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Source: Google AI Blog