Stochastic Gradient Line Bayesian Optimization: Reducing Measurement Shots in Optimizing Parameterized Quantum Circuits

Tamiya, Shiro; Yamasaki, Hayata

doi:10.48550/arxiv.2111.07952

Cited by 5 publications

(4 citation statements)

References 64 publications

(129 reference statements)

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“…Note added -In independent recent work 50 another optimisation algorithm, called SGSLBO (Stochastic Gradient Line Bayesian Optimization), is proposed for VQE that is at first glance similar to ours. However, this algorithm is based on the use of stochastic gradient descent to determine the gradient direction paired with Bayesian optimisation for a line search along the gradient direction.…”

Section: Appendix D: Variational Optimisermentioning

confidence: 84%

Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

Stanisic¹,

Bosse²,

Gambetta³

et al. 2021

Preprint

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The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the reach of near-term quantum hardware. Here we show experimentally that an efficient, low-depth variational quantum algorithm with few parameters can reproduce important qualitative features of medium-size instances of the Fermi-Hubbard model. We address 1 × 8 and 2 × 4 instances on 16 qubits on a superconducting quantum processor, substantially larger than previous work based on less scalable compression techniques, and going beyond the family of 1D Fermi-Hubbard instances, which are solvable classically. Consistent with predictions for the ground state, we observe the onset of the metal-insulator transition and Friedel oscillations in 1D, and antiferromagnetic order in both 1D and 2D. We use a variety of errormitigation techniques, including symmetries of the Fermi-Hubbard model and a recently developed technique tailored to simulating fermionic systems. We also introduce a new variational optimisation algorithm based on iterative Bayesian updates of a local surrogate model. Our scalable approach is a first step to using near-term quantum computers to determine low-energy properties of stronglycorrelated electronic systems that cannot be solved exactly by classical computers.

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Section: Appendix D: Variational Optimisermentioning

confidence: 84%

Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

Stanisic¹,

Bosse²,

Gambetta³

et al. 2021

Preprint

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show abstract

“…2 In the quantum computing setting, adopting an algorithm like SHOALS translates to significantly lower total time, since certain large parts of the latency costs are paid per iteration, rather than per shot, at the expense of potentially higher (but dynamic) numbers of shots. We note that a recent paper on another classical optimizer for VQAs employs a Bayesian line search [39], which is fundamentally different from the line search considered in this paper.…”

Section: Our Contributionsmentioning

confidence: 93%

Latency considerations for stochastic optimizers in variational quantum algorithms

Menickelly

Otten

2023

Quantum

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Variational quantum algorithms, which have risen to prominence in the noisy intermediate-scale quantum setting, require the implementation of a stochastic optimizer on classical hardware. To date, most research has employed algorithms based on the stochastic gradient iteration as the stochastic classical optimizer. In this work we propose instead using stochastic optimization algorithms that yield stochastic processes emulating the dynamics of classical deterministic algorithms. This approach results in methods with theoretically superior worst-case iteration complexities, at the expense of greater per-iteration sample (shot) complexities. We investigate this trade-off both theoretically and empirically and conclude that preferences for a choice of stochastic optimizer should explicitly depend on a function of both latency and shot execution times.

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“…Convergence to a local minimum can be guaranteed by the use of backtracking, where η is steadily decreased during the course of the calculation [133]. Alternatively, the step size can be selected by using Bayesian optimization to perform a line search [134].…”

Section: Optimizationmentioning

confidence: 99%

Preparation of the SU(3) lattice Yang-Mills vacuum with variational quantum methods

Ciavarella

Chernyshev

2022

Phys. Rev. D

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Studying QCD and other gauge theories on quantum hardware requires the preparation of physically interesting states. The Variational Quantum Eigensolver (VQE) provides a way of performing vacuum state preparation on quantum hardware. In this work, VQE is applied to pure SU(3) lattice Yang-Mills on a single plaquette and one dimensional plaquette chains. Bayesian optimization and gradient descent were investigated for performing the classical optimization. Ansatz states for plaquette chains are constructed in a scalable manner from smaller systems using domain decomposition and a stitching procedure analogous to the Density Matrix Renormalization Group (DMRG). Small examples are performed on IBM's superconducting Manila processor. CONTENTSA. Hardware Calculations 14 B. Bayesian Optimization 15 C. Plaquette Chain Tensor Network 16 D. Data from IBM's Manila Processor 17 References 18

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Stochastic Gradient Line Bayesian Optimization: Reducing Measurement Shots in Optimizing Parameterized Quantum Circuits

Cited by 5 publications

References 64 publications

Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

Latency considerations for stochastic optimizers in variational quantum algorithms

Preparation of the SU(3) lattice Yang-Mills vacuum with variational quantum methods

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