Quantum supremacy using a programmable superconducting processor.

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy8-14 for this specific computational task, heralding a much-anticipated computing paradigm.

What the foundations of quantum computer science teach us about chemistry.

With the rapid development of quantum technology, one of the leading applications that has been identified is the simulation of chemistry. Interestingly, even before full scale quantum computers are available, quantum computer science has exhibited a remarkable string of results that directly impact what is possible in a chemical simulation with any computer. Some of these results even impact our understanding of chemistry in the real world. In this Perspective, we take the position that direct chemical simulation is best understood as a digital experiment. While on the one hand, this clarifies the power of quantum computers to extend our reach, it also shows us the limitations of taking such an approach too directly. Leveraging results that quantum computers cannot outpace the physical world, we build to the controversial stance that some chemical problems are best viewed as problems for which no algorithm can deliver their solution, in general, known in computer science as undecidable problems. This has implications for the predictive power of thermodynamic models and topics such as the ergodic hypothesis. However, we argue that this Perspective is not defeatist but rather helps shed light on the success of existing chemical models such as transition state theory, molecular orbital theory, and thermodynamics as models that benefit from data. We contextualize recent results, showing that data-augmented models are a more powerful rote simulation. These results help us appreciate the success of traditional chemical theory and anticipate new models learned from experimental data. Not only can quantum computers provide data for such models, but they can also extend the class and power of models that utilize data in fundamental ways. These discussions culminate in speculation on new ways for quantum computing and chemistry to interact and our perspective on the eventual roles of quantum computers in the future of chemistry.

Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics.

We introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism naturally leads to an algorithm to parallelize quantum simulation over time. We draw an explicit connection between previously known time-dependent variational principles and the time-embedded variational principle presented. Sample calculations are presented, applying the idea to a hydrogen molecule and the spin degrees of freedom of a model inorganic compound, demonstrating the parallel speedup of our method as well as its flexibility in applying ground-state methodologies. Finally, we take advantage of the unique perspective of this variational principle to examine the error of basis approximations in quantum dynamics.

Quantum advantage in learning from experiments.

Quantum technology promises to revolutionize how we learn about the physical world. An experiment that processes quantum data with a quantum computer could have substantial advantages over conventional experiments in which quantum states are measured and outcomes are processed with a classical computer. We proved that quantum machines could learn from exponentially fewer experiments than the number required by conventional experiments. This exponential advantage is shown for predicting properties of physical systems, performing quantum principal component analysis, and learning about physical dynamics. Furthermore, the quantum resources needed for achieving an exponential advantage are quite modest in some cases. Conducting experiments with 40 superconducting qubits and 1300 quantum gates, we demonstrated that a substantial quantum advantage is possible with today's quantum processors.

Power of data in quantum machine learning.

The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits.

Decoding quantum errors with subspace expansions.

With rapid developments in quantum hardware comes a push towards the first practical applications. While fully fault-tolerant quantum computers are not yet realized, there may exist intermediate forms of error correction that enable practical applications. In this work, we consider the idea of post-processing error decoders using existing quantum codes, which mitigate errors on logical qubits using post-processing without explicit syndrome measurements or additional qubits beyond the encoding overhead. This greatly simplifies the experimental exploration of quantum codes on real, near-term devices, removing the need for locality of syndromes or fast feed-forward. We develop the theory of the method and demonstrate it on an example with the perfect [[5, 1, 3]] code, which exhibits a pseudo-threshold of p ≈ 0.50 under a single qubit depolarizing channel applied to all qubits. We also provide a demonstration of improved performance on an unencoded hydrogen molecule.

Barren plateaus in quantum neural network training landscapes.

Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum simulation, optimization, and machine learning. Due to its simplicity and hardware efficiency, random circuits are often proposed as initial guesses for exploring the space of quantum states. We show that the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. Specifically, we show that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. We argue that this is related to the 2-design characteristic of random circuits, and that solutions to this problem must be studied.

Witnessing eigenstates for quantum simulation of Hamiltonian spectra.

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an "eigenstate witness" and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers.

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation.

Calculating molecular energies is likely to be one of the first useful applications to achieve quantum supremacy, performing faster on a quantum than a classical computer. However, if future quantum devices are to produce accurate calculations, errors due to environmental noise and algorithmic approximations need to be characterized and reduced. In this study, we use the high performance qHiPSTER software to investigate the effects of environmental noise on the preparation of quantum chemistry states. We simulated 18 16-qubit quantum circuits under environmental noise, each corresponding to a unitary coupled cluster state preparation of a different molecule or molecular configuration. Additionally, we analyze the nature of simple gate errors in noise-free circuits of up to 40 qubits. We find that, in most cases, the Jordan-Wigner (JW) encoding produces smaller errors under a noisy environment as compared to the Bravyi-Kitaev (BK) encoding. For the JW encoding, pure dephasing noise is shown to produce substantially smaller errors than pure relaxation noise of the same magnitude. We report error trends in both molecular energy and electron particle number within a unitary coupled cluster state preparation scheme, against changes in nuclear charge, bond length, number of electrons, noise types, and noise magnitude. These trends may prove to be useful in making algorithmic and hardware-related choices for quantum simulation of molecular energies.

Exploiting Locality in Quantum Computation for Quantum Chemistry.

Accurate prediction of chemical and material properties from first-principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route toward highly accurate solutions with polynomial cost; however, this solution still carries a large overhead. In this Perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provides numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.