The theory of variational hybrid quantum-classical algorithms

McClean, Jarrod R.; Romero, Jonathan; Babbush, Ryan; Aspuru‐Guzik, Alán

doi:10.1088/1367-2630/18/2/023023

Cited by 1,827 publications

(1,879 citation statements)

References 94 publications

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“…In turn, it is expected that in the near term the progress in quantum experiments will lead to devices with dynamics, which are beyond what can be simulated with a conventional computer. This leads to the question: what computational tasks could be accomplished with only limited, or no error correction?The suggestions of near-term applications in such quantum devices mostly center around quantum simulations with short-depth circuit [10][11][12] and approximate optimization algorithms [13]. Furthermore, certain problems in material simulation may be tackled by hybrid quantum-classical algorithms [14].…”

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confidence: 99%

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Error Mitigation for Short-Depth Quantum Circuits

Temme¹,

Bravyi²,

Gambetta³

2017

Phys. Rev. Lett.

1,025

987

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Two schemes are presented that mitigate the effect of errors and decoherence in short-depth quantum circuits. The size of the circuits for which these techniques can be applied is limited by the rate at which the errors in the computation are introduced. Near-term applications of early quantum devices, such as quantum simulations, rely on accurate estimates of expectation values to become relevant. Decoherence and gate errors lead to wrong estimates of the expectation values of observables used to evaluate the noisy circuit. The two schemes we discuss are deliberately simple and don't require additional qubit resources, so to be as practically relevant in current experiments as possible. The first method, extrapolation to the zero noise limit, subsequently cancels powers of the noise perturbations by an application of Richardson's deferred approach to the limit. The second method cancels errors by resampling randomized circuits according to a quasi-probability distribution.From the time quantum computation generated wide spread interest, the strongest objection to its viability was the sensitivity to errors and noise. In an early paper, William Unruh [1] found that the coupling to the environment sets an ultimate time and size limit for any quantum computation. This initially curbed the hopes that the full advantage of quantum computing could be harnessed, since it set limits on the scalability of any algorithm. This problem was, at least in theory, remedied with the advent of quantum error correction [2][3][4]. It was proven that if both the decoherence and the imprecision of gates could be reduced below a finite threshold value, then quantum computation could be performed indefinitely [5,6]. Although it is the ultimate goal to reach this threshold in an experiment that is scalable to larger sizes, the overhead that is needed to implement a fully fault-tolerant gate set with current codes [7] seems prohibitively large [8,9]. In turn, it is expected that in the near term the progress in quantum experiments will lead to devices with dynamics, which are beyond what can be simulated with a conventional computer. This leads to the question: what computational tasks could be accomplished with only limited, or no error correction?The suggestions of near-term applications in such quantum devices mostly center around quantum simulations with short-depth circuit [10][11][12] and approximate optimization algorithms [13]. Furthermore, certain problems in material simulation may be tackled by hybrid quantum-classical algorithms [14]. In most such applications, the task can be abstracted to applying a short-depth quantum circuits to some simple initial state and then estimating the expectation value of some observable after the circuit has been applied. This estimation must be accurate enough to achieve a simulation precision comparable or exceeding that of classical algorithms. Yet, although the quantum system evolves coherently for the most part of the short-depth circuit, the effects of decoherence already become apparent...

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mentioning

confidence: 99%

“…The suggestions of near-term applications in such quantum devices mostly center around quantum simulations with short-depth circuit [10][11][12] and approximate optimization algorithms [13]. Furthermore, certain problems in material simulation may be tackled by hybrid quantum-classical algorithms [14].…”

mentioning

confidence: 99%

Error Mitigation for Short-Depth Quantum Circuits

Temme¹,

Bravyi²,

Gambetta³

2017

Phys. Rev. Lett.

1,025

987

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“…The same quantum hardware has been used to show a hybrid quantum‐classical approach to the simulation of the Schwinger model . The latter belongs to the class of variational optimization algorithms commonly employed in quantum chemistry, an approach now commonly defined Variational Quantum Eigensolver (VQE). In fact, the latter methods have been recently applied to accurately calculate the ground state energy of simple molecules .…”

Section: Experimental Achievements and Prospective Technologiesmentioning

confidence: 99%

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

et al. 2019

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The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have become available for simulations and benchmarking, with up to few tens of qubits that can be reliably initialized, controlled, and measured. The present Review aims at giving a comprehensive outlook on the state‐of‐the‐art capabilities offered from these near‐term noisy devices as universal quantum simulators, that is, programmable quantum computers potentially able to calculate the time evolution of many physical models. First, a pedagogic overview on the basic theoretical background pertaining digital quantum simulations is given, with a focus on hardware‐dependent mapping of spin‐type Hamiltonians into the corresponding quantum circuit as a key initial step toward simulating more complex models. Then, the main experimental achievements obtained in the last decade are reviewed, focusing on the digital quantum simulation of such spin models by employing two leading quantum architectures. Their performances are compared, and future challenges are outlined, also in view of prospective hybrid technologies, towards the ultimate goal of reaching the long‐sought quantum advantage for the simulation of complex many‐body models in the physical sciences.

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“…Moreover, the implementation of a full quantum eigensolver [35][36][37][38] using near-future quantum computers seems impractical due to the number of needed resources [39]. The emergence of hybrid classical-quantum algorithms in the past few years [40][41][42][43][44][45][46] opens the door to the development of useful eigensolvers. Nevertheless, these works are mainly focused on the eigenvalues, eigenvectors, and properties of quantum systems such as molecules, being the characterization of a physical interaction less studied.…”

Section: Introductionmentioning

confidence: 99%

Reinforcement learning for semi-autonomous approximate quantum eigensolver

Albarrán-Arriagada

Retamal

Solano

et al. 2020

Mach. Learn.: Sci. Technol.

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The characterization of an operator by its eigenvectors and eigenvalues allows us to know its action over any quantum state. Here, we propose a protocol to obtain an approximation of the eigenvectors of an arbitrary Hermitian quantum operator. This protocol is based on measurement and feedback processes, which characterize a reinforcement learning protocol. Our proposal is composed of two systems, a black box named environment and a quantum state named agent. The role of the environment is to change any quantum state by a unitary matrixˆ= tHermitian operator, and τ is a real parameter. The agent is a quantum state which adapts to some eigenvector of  E by repeated interactions with the environment, feedback process, and semi-random rotations. With this proposal, we can obtain an approximation of the eigenvectors of a random qubit operator with average fidelity over 90% in less than 10 iterations, and surpass 98% in less than 300 iterations. Moreover, for the two-qubit cases, the four eigenvectors are obtained with fidelities above 89% in 8000 iterations for a random operator, and fidelities of 99% for an operator with the Bell states as eigenvectors. This protocol can be useful to implement semi-autonomous quantum devices which should be capable of extracting information and deciding with minimal resources and without human intervention.

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The theory of variational hybrid quantum-classical algorithms

Cited by 1,827 publications

References 94 publications

Error Mitigation for Short-Depth Quantum Circuits

Error Mitigation for Short-Depth Quantum Circuits

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

Reinforcement learning for semi-autonomous approximate quantum eigensolver

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