Tag Archives: Quantum AI

Google Research, 2022 & beyond: Natural sciences

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

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

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

Using machine learning to unlock mysteries in biology

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


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

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

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

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


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

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

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

Using quantum computing for new physics discoveries

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

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

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

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

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


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


Google Research, 2022 & beyond

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

Source: Google AI Blog

Amplification at the Quantum limit

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

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

Why microwave amplifiers?

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

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

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

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


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

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

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

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

Conclusion and future directions

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


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

Source: Google AI Blog

Formation of Robust Bound States of Interacting Photons

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

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

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


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

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

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

Bound Photons

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

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

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

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

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

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

Bound States Behave Like Single Composite Particles

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

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

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

Breaking Integrability

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

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

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

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


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


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

Source: Google AI Blog

Quantum Advantage in Learning from Experiments

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Source: Google AI Blog

Hybrid Quantum Algorithms for Quantum Monte Carlo

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Source: Google AI Blog

Resolving High-Energy Impacts on Quantum Processors

Quantum processors are made of superconducting quantum bits (qubits) that — being quantum objects — are highly susceptible to even tiny amounts of environmental noise. This noise can cause errors in quantum computation that need to be addressed to continue advancing quantum computers. Our Sycamore processors are installed in specially designed cryostats, where they are sealed away from stray light and electromagnetic fields and are cooled down to very low temperatures to reduce thermal noise.

However, the world is full of high-energy radiation. In fact, there’s a tiny background of high-energy gamma rays and muons that pass through everything around us all the time. While these particles interact so weakly that they don’t cause any harm in our day-to-day lives, qubits are sensitive enough that even weak particle interactions can cause significant interference.

In “Resolving Catastrophic Error Bursts from Cosmic Rays in Large Arrays of Superconducting Qubits”, published in Nature Physics, we identify the effects of these high-energy particles when they impact the quantum processor. To detect and study individual impact events, we use new techniques in rapid, repetitive measurement to operate our processor like a particle detector. This allows us to characterize the resulting burst of errors as they spread through the chip, helping to better understand this important source of correlated errors.

The Dynamics of a High-Energy Impact
The Sycamore quantum processor is constructed with a very thin layer of superconducting aluminum on a silicon substrate, onto which a pattern is etched to define the qubits. At the center of each qubit is the Josephson junction, a superconducting component that defines the distinct energy levels of the qubit, which are used for computation. In a superconducting metal, electrons bind together into a macroscopic, quantum state, which allows electrons to flow as a current with zero resistance (a supercurrent). In superconducting qubits, information is encoded in different patterns of oscillating supercurrent going back and forth through the Josephson junction.

If enough energy is added to the system, the superconducting state can be broken up to produce quasiparticles. These quasiparticles are a problem, as they can absorb energy from the oscillating supercurrent and jump across the Josephson junction, which changes the qubit state and produces errors. To prevent any energy from being absorbed by the chip and producing quasiparticles, we use extensive shielding for electric and magnetic fields, and powerful cryogenic refrigerators to keep the chip near absolute zero temperature, thus minimizing the thermal energy.

A source of energy that we can’t effectively shield against is high-energy radiation, which includes charged particles and photons that can pass straight through most materials. One source of these particles are tiny amounts of radioactive elements that can be found everywhere, e.g., in building materials, the metal that makes up our cryostats, and even in the air. Another source is cosmic rays, which are extremely energetic particles produced by supernovae and black holes. When cosmic rays impact the upper atmosphere, they create a shower of high-energy particles that can travel all the way down to the surface and through our chip. Between radioactive impurities and cosmic ray showers, we expect a high energy particle to pass through a quantum chip every few seconds.

When a high-energy impact event occurs, energy spreads through the chip in the form of phonons. When these arrive at the superconducting qubit layer, they break up the superconducting state and produce quasiparticles, which cause the qubit errors we observe.

When one of these particles impinges on the chip, it passes straight through and deposits a small amount of its energy along its path through the substrate. Even a small amount of energy from these particles is a very large amount of energy for the qubits. Regardless of where the impact occurs, the energy quickly spreads throughout the entire chip through quantum vibrations called phonons. When these phonons hit the aluminum layer that makes up the qubits, they have more than enough energy to break the superconducting state and produce quasiparticles. So many quasiparticles are produced that the probability of the qubits interacting with one becomes very high. We see this as a sudden and significant increase in errors over the whole chip as those quasiparticles absorb energy from the qubits. Eventually, as phonons escape and the chip cools, these quasiparticles recombine back into the superconducting state, and the qubit error rates slowly return to normal.

A high-energy particle impact (at time = 0 ms) on a patch of the quantum processor, showing error rates for each qubit over time. The event starts by rapidly spreading error over the whole chip, before saturating and then slowly returning to equilibrium.

Detecting Particles with a Computer
The Sycamore processor is designed to perform quantum error correction (QEC) to improve the error rates and enable it to execute a variety of quantum algorithms. QEC provides an effective way of identifying and mitigating errors, provided they are sufficiently rare and independent. However, in the case of a high-energy particle going through the chip, all of the qubits will experience high error rates until the event cools off, producing a correlated error burst that QEC won’t be able to correct. In order to successfully perform QEC, we first have to understand what these impact events look like on the processor, which requires operating it like a particle detector.

To do so, we take advantage of recent advances in qubit state preparation and measurement to quickly prepare each qubit in their excited state, similar to flipping a classical bit from 0 to 1. We then wait for a short idle time and measure whether they are still excited. If the qubits are behaving normally, almost all of them will be. Further, the qubits that experience a decay out of their excited state won’t be correlated, meaning the qubits that have errors will be randomly distributed over the chip.

However, during the experiment we occasionally observe large error bursts, where all the qubits on the chip suddenly become more error prone all at once. This correlated error burst is a clear signature of a high-energy impact event. We also see that, while all qubits on the chip are affected by the event, the qubits with the highest error rates are all concentrated in a “hotspot” around the impact site, where slightly more energy is deposited into the qubit layer by the spreading phonons.

To detect high-energy impacts, we rapidly prepare the qubits in an excited state, wait a little time, and then check if they’ve maintained their state. An impact produces a correlated error burst, where all the qubits show a significantly elevated error rate, as shown around time = 8 seconds above.

Next Steps
Because these error bursts are severe and quickly cover the whole chip, they are a type of correlated error that QEC is unable to correct. Therefore, it’s very important to find a solution to mitigate these events in future processors that are expected to rely on QEC.

Shielding against these particles is very difficult and typically requires careful engineering and design of the cryostat and many meters of shielding, which becomes more impractical as processors grow in size. Another approach is to modify the chip, allowing it to tolerate impacts without causing widespread correlated errors. This is an approach taken in other complex superconducting devices like detectors for astronomical telescopes, where it’s not possible to use shielding. Examples of such mitigation strategies include adding additional metal layers to the chip to absorb phonons and prevent them from getting to the qubit, adding barriers in the chip to prevent phonons spreading over long distances, and adding traps for quasiparticles in the qubits themselves. By employing these techniques, future processors will be much more robust to these high-energy impact events.

As the error rates of quantum processors continue to decrease, and as we make progress in building a prototype of an error-corrected logical qubit, we're increasingly pushed to study more exotic sources of error. While QEC is a powerful tool for correcting many kinds of errors, understanding and correcting more difficult sources of correlated errors will become increasingly important. We’re looking forward to future processor designs that can handle high energy impacts and enable the first experimental demonstrations of working quantum error correction.

This work wouldn’t have been possible without the contributions of the entire Google Quantum AI Team, especially those who worked to design, fabricate, install and calibrate the Sycamore processors used for this experiment. Special thanks to Rami Barends and Lev Ioffe, who led this project.

Source: Google AI Blog

Demonstrating the Fundamentals of Quantum Error Correction

The Google Quantum AI team has been building quantum processors made of superconducting quantum bits (qubits) that have achieved the first beyond-classical computation, as well as the largest quantum chemical simulations to date. However, current generation quantum processors still have high operational error rates — in the range of 10-3 per operation, compared to the 10-12 believed to be necessary for a variety of useful algorithms. Bridging this tremendous gap in error rates will require more than just making better qubits — quantum computers of the future will have to use quantum error correction (QEC).

The core idea of QEC is to make a logical qubit by distributing its quantum state across many physical data qubits. When a physical error occurs, one can detect it by repeatedly checking certain properties of the qubits, allowing it to be corrected, preventing any error from occurring on the logical qubit state. While logical errors may still occur if a series of physical qubits experience an error together, this error rate should exponentially decrease with the addition of more physical qubits (more physical qubits need to be involved to cause a logical error). This exponential scaling behavior relies on physical qubit errors being sufficiently rare and independent. In particular, it’s important to suppress correlated errors, where one physical error simultaneously affects many qubits at once or persists over many cycles of error correction. Such correlated errors produce more complex patterns of error detections that are more difficult to correct and more easily cause logical errors.

Our team has recently implemented the ideas of QEC in our Sycamore architecture using quantum repetition codes. These codes consist of one-dimensional chains of qubits that alternate between data qubits, which encode the logical qubit, and measure qubits, which we use to detect errors in the logical state. While these repetition codes can only correct for one kind of quantum error at a time1, they contain all of the same ingredients as more sophisticated error correction codes and require fewer physical qubits per logical qubit, allowing us to better explore how logical errors decrease as logical qubit size grows.

In “Removing leakage-induced correlated errors in superconducting quantum error correction”, published in Nature Communications, we use these repetition codes to demonstrate a new technique for reducing the amount of correlated errors in our physical qubits. Then, in “Exponential suppression of bit or phase flip errors with repetitive error correction”, published in Nature, we show that the logical errors of these repetition codes are exponentially suppressed as we add more and more physical qubits, consistent with expectations from QEC theory.

Layout of the repetition code (21 qubits, 1D chain) and distance-2 surface code (7 qubits) on the Sycamore device.

Leaky Qubits
The goal of the repetition code is to detect errors on the data qubits without measuring their states directly. It does so by entangling each pair of data qubits with their shared measure qubit in a way that tells us whether those data qubit states are the same or different (i.e., their parity) without telling us the states themselves. We repeat this process over and over in rounds that last only one microsecond. When the measured parities change between rounds, we’ve detected an error.

However, one key challenge stems from how we make qubits out of superconducting circuits. While a qubit needs only two energy states, which are usually labeled |0 and |1, our devices feature a ladder of energy states, |0, |1, |2, |3, and so on. We use the two lowest energy states to encode our qubit with information to be used for computation (we call these the computational states). We use the higher energy states (|2, |3 and higher) to help achieve high-fidelity entangling operations, but these entangling operations can sometimes allow the qubit to “leak” into these higher states, earning them the name leakage states.

Population in the leakage states builds up as operations are applied, which increases the error of subsequent operations and even causes other nearby qubits to leak as well — resulting in a particularly challenging source of correlated error. In our early 2015 experiments on error correction, we observed that as more rounds of error correction were applied, performance declined as leakage began to build.

Mitigating the impact of leakage required us to develop a new kind of qubit operation that could “empty out” leakage states, called multi-level reset. We manipulate the qubit to rapidly pump energy out into the structures used for readout, where it will quickly move off the chip, leaving the qubit cooled to the |0 state, even if it started in |2 or |3. Applying this operation to the data qubits would destroy the logical state we’re trying to protect, but we can apply it to the measure qubits without disturbing the data qubits. Resetting the measure qubits at the end of every round dynamically stabilizes the device so leakage doesn’t continue to grow and spread, allowing our devices to behave more like ideal qubits.

Applying the multi-level reset gate to the measure qubits almost totally removes leakage, while also reducing the growth of leakage on the data qubits.

Exponential Suppression
Having mitigated leakage as a significant source of correlated error, we next set out to test whether the repetition codes give us the predicted exponential reduction in error when increasing the number of qubits. Every time we run our repetition code, it produces a collection of error detections. Because the detections are linked to pairs of qubits rather than individual qubits, we have to look at all of the detections to try to piece together where the errors have occurred, a procedure known as decoding. Once we’ve decoded the errors, we then know which corrections we need to apply to the data qubits. However, decoding can fail if there are too many error detections for the number of data qubits used, resulting in a logical error.

To test our repetition codes, we run codes with sizes ranging from 5 to 21 qubits while also varying the number of error correction rounds. We also run two different types of repetition codes — either a phase-flip code or bit-flip code — that are sensitive to different kinds of quantum errors. By finding the logical error probability as a function of the number of rounds, we can fit a logical error rate for each code size and code type. In our data, we see that the logical error rate does in fact get suppressed exponentially as the code size is increased.

Probability of getting a logical error after decoding versus number of rounds run, shown for various sizes of phase-flip repetition code.

We can quantify the error suppression with the error scaling parameter Lambda (Λ), where a Lambda value of 2 means that we halve the logical error rate every time we add four data qubits to the repetition code. In our experiments, we find Lambda values of 3.18 for the phase-flip code and 2.99 for the bit-flip code. We can compare these experimental values to a numerical simulation of the expected Lambda based on a simple error model with no correlated errors, which predicts values of 3.34 and 3.78 for the bit- and phase-flip codes respectively.

Logical error rate per round versus number of qubits for the phase-flip (X) and bit-flip (Z) repetition codes. The line shows an exponential decay fit, and Λ is the scale factor for the exponential decay.

This is the first time Lambda has been measured in any platform while performing multiple rounds of error detection. We’re especially excited about how close the experimental and simulated Lambda values are, because it means that our system can be described with a fairly simple error model without many unexpected errors occurring. Nevertheless, the agreement is not perfect, indicating that there’s more research to be done in understanding the non-idealities of our QEC architecture, including additional sources of correlated errors.

What’s Next
This work demonstrates two important prerequisites for QEC: first, the Sycamore device can run many rounds of error correction without building up errors over time thanks to our new reset protocol, and second, we were able to validate QEC theory and error models by showing exponential suppression of error in a repetition code. These experiments were the largest stress test of a QEC system yet, using 1000 entangling gates and 500 qubit measurements in our largest test. We’re looking forward to taking what we learned from these experiments and applying it to our target QEC architecture, the 2D surface code, which will require even more qubits with even better performance.

1A true quantum error correcting code would require a two dimensional array of qubits in order to correct for all of the errors that could occur. 

Source: Google AI Blog

Achieving Precision in Quantum Material Simulations

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

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

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

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

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

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

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

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

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

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

Source: Google AI Blog

Quantum Machine Learning and the Power of Data

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

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

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

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

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

Geometric Test for Quantum Learning Advantage

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Source: Google AI Blog

Scaling Up Fundamental Quantum Chemistry Simulations on Quantum Hardware

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

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

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

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

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

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

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

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

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

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

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

Source: Google AI Blog