Low-depth circuit ansatz for preparing correlated fermionic states on a quantum computer

Dallaire-Demers, Pierre-Luc; Romero, Jonathan; Veis, Libor; Sim, Sukin; Aspuru‐Guzik, Alán

doi:10.1088/2058-9565/ab3951

Cited by 118 publications

(126 citation statements)

References 94 publications

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“…next-neighbor) qubit connectivity. In [121], a similar ansatz is introduced, also with linear gate depth which is equivalent to the fermionic swap network from [41] with a different variational parameter initialization.…”

Section: Discussionmentioning

confidence: 99%

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator

et al. 2018

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Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multi-qubit quantum simulators.

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Section: Discussionmentioning

confidence: 99%

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator

et al. 2018

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“…In an effort to improve or create HQC algorithms, numerous studies have developed better ansatze, in terms of accuracy, scalability, and implementability on near‐term devices for specific applications . Many proposals have been either theoretically motivated but impractical, or practical but largely ad hoc.…”

Section: Discussionmentioning

confidence: 99%

Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms

2019

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Parameterized quantum circuits (PQCs) play an essential role in the performance of many variational quantum algorithms. One challenge in implementing such algorithms is choosing an effective circuit that well represents the solution space while maintaining a low circuit depth and parameter count. To characterize and identify expressible, yet compact, circuits, several descriptors are proposed, including expressibility and entangling capability, that are statistically estimated from classical simulations. These descriptors are computed for different circuit structures, varying the qubit connectivity and selection of gates. From these simulations, circuit fragments that perform well with respect to the descriptors are identified. In particular, a substantial improvement in performance of two‐qubit gates in a ring or all‐to‐all connected arrangement, compared to that of those on a line, is observed. Furthermore, improvement in both descriptors is achieved by sequences of controlled X‐rotation gates compared to sequences of controlled Z‐rotation gates. In addition, it is investigated how expressibility “saturates” with increased circuit depth, finding that the rate and saturated value appear to be distinguishing features of a PQC. While the correlation between each descriptor and algorithm performance remains to be investigated, methods and results from this study can be useful for algorithm development and design of experiments.

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“…where g a,μ ∈ R and P a,μ ∈ P. We often use this form of parametrized quantum circuits, for example see Refs. [40][41][42][43].…”

Section: A Notations and Assumptionsmentioning

confidence: 99%

Theory of analytical energy derivatives for the variational quantum eigensolver

Mitarai

Nakagawa²,

Mizukami

2020

Phys. Rev. Research

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The variational quantum eigensolver (VQE) and its variants, which is a method for finding eigenstates and eigenenergies of a given Hamiltonian, are appealing applications of near-term quantum computers. Although the eigenenergies are certainly important quantities which determine properties of a given system, their derivatives with respect to parameters of the system, such as positions of nuclei if we target a quantum chemistry problem, are also crucial to analyze the system. Here, we describe methods to evaluate analytical derivatives of the eigenenergy of a given Hamiltonian, including the excited state energy as well as the ground-state energy, with respect to the system parameters in the framework of the VQE. We give explicit, low-depth quantum circuits which can measure essential quantities to evaluate energy derivatives, incorporating with proof-of-principle numerical simulations. This work extends the theory of the variational quantum eigensolver, by enabling it to measure more physical properties of a quantum system than before and to explore chemical reactions.

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Low-depth circuit ansatz for preparing correlated fermionic states on a quantum computer

Cited by 118 publications

References 94 publications

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator

Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms

Theory of analytical energy derivatives for the variational quantum eigensolver

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