Variational Quantum Eigensolver for SU($N$) Fermions

Consiglio, Mirko; Chetcuti, Wayne J.; Bravo-Prieto, Carlos; Ramos-Calderer, Sergi; Minguzzi, Anna; Latorre, José I.; Amico, Luigi; Apollaro, Tony J. G.

doi:10.48550/arxiv.2106.15552

Cited by 2 publications

(2 citation statements)

References 55 publications

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“…Nevertheless, we will see as our considerations are in agreement with more structured studies in literature applied to parametrized quantum circuits [41,42]. Further, we point to reference [43] where alternative strategies are discussed to quantify the performance of variational ansatz.…”

Section: Variational Network Assessmentsupporting

confidence: 82%

Quantum computing for classical problems: variational quantum eigensolver for activated processes

et al. 2021

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The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker-Plank-Smoluchowski equation models the time evolution of the probability density of selected degrees of freedom in the diffusive regime and it is a workhorse of physical chemistry. In this paper, we report the development and implementation of a Variational Quantum Eigensolver procedure to solve the Fokker-Planck-Smoluchowski eigenvalue problem. We show that such an algorithm, typically adopted to address quantum chemistry problems, can be applied effectively to classical systems paving the way to new applications of quantum computers. We compute the conformational transition rate in a linear chain of rotors experiencing nearest-neighbor interaction. We provide a method to encode on the quantum computer the probability distribution for a given conformation of the chain and assess its scalability in terms of operations. Performance analysis on noisy quantum emulators and quantum devices (IBMQ Santiago) is provided for a small chain showing results in good agreement with the classical benchmark without further addition of any error mitigation technique.

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Section: Variational Network Assessmentsupporting

confidence: 82%

Quantum computing for classical problems: variational quantum eigensolver for activated processes

et al. 2021

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“…The Variational Quantum Eigensolver (VQE), is a specific variational algorithm that aims to minimize the expectation value of a given Hamiltonian. The VQE is sufficiently flexible to solve many optimization problems, including MAXCUT [8,9], portfolio optimisation [10], financial transaction settlement [11], and finding the ground state of solid-state Hamiltonians [12] or interacting fermions [13].…”

Section: Introductionmentioning

confidence: 99%

Clifford Circuit Initialisation for Variational Quantum Algorithms

Cheng¹,

Khosla²,

Self³

et al. 2022

Preprint

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We present an initialisation method for variational quantum algorithms applicable to intermediate scale quantum computers. The method uses simulated annealing of the efficiently simulable Clifford parameter points as a pre-optimisation to find a low energy initial condition. We numerically demonstrate the effectiveness of the technique, and how it depends on Hamiltonian structure, number of qubits and circuit depth. While a range of different problems are considered, we note that the method is particularly useful for quantum chemistry problems. This presented method could help achieve a quantum advantage in noisy or fault-tolerant intermediate scale devices, even though we prove in general that the method is not arbitrarily scalable.

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Variational Quantum Eigensolver for SU($N$) Fermions

Cited by 2 publications

References 55 publications

Quantum computing for classical problems: variational quantum eigensolver for activated processes

Quantum computing for classical problems: variational quantum eigensolver for activated processes

Clifford Circuit Initialisation for Variational Quantum Algorithms

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