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arXiv:2411.13742

Benchmarking a wide range of optimisers for solving the Fermi-Hubbard model using the variational quantum eigensolver

Benjamin D. M. Jones, Lana Mineh, Ashley Montanaro

Published Nov 20, 2024• 0 citations
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Abstract

Data used in the paper "Benchmarking a wide range of optimisers for solving the Fermi-Hubbard model using the variational quantum eigensolver" by Benjamin D.M. Jones, Lana Mineh, and Ashley Montanaro, available here: https://arxiv.org/abs/2411.13742. See the README.md file for details on how the data is organised, and data.zip for the full data (~37GB when uncompressed).

DOI
10.48550/arxiv.2411.13742

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Data used in the paper "Benchmarking a wide range of optimisers for solving the Fermi-Hubbard model using the variational quantum eigensolver" by Benjamin D.M. Jones, Lana Mineh, and Ashley Montanaro, available here: https://arxiv.org/abs/2411.13742. See the README.md file for details on how the data is organised, and data.zip for the full data (~37GB when uncompressed).
Abstract We numerically benchmark 30 optimisers on 372 instances of the variational quantum eigensolver for solving the Fermi–Hubbard system with the Hamiltonian variational ansatz. We rank the optimisers with respect to metrics such as final energy achieved and function calls needed to get within a certain tolerance level, and find that the best-performing optimisers are variants of gradient descent such as Momentum and ADAM (using finite difference), SPSA, CMAES, and BayesMGD. We perform gradient analysis, and observe that the step size for finite difference has a very significant impact. We also consider using simultaneous perturbation (inspired by SPSA) as a gradient subroutine: here finite difference can lead to a more precise estimate of the ground state but uses more calls, whereas simultaneous perturbation can converge quicker but may be less precise in the later stages. Finally, we study the quantum natural gradient algorithm: we implement this method for one-dimensional Fermi–Hubbard systems, and find that whilst it can reach a lower energy with fewer iterations, this improvement is typically lost when taking total function calls into account. Our method involves performing careful hyperparameter sweeping on 4 instances. We present a variety of analysis and figures, detailed optimiser notes, and discuss future directions.
Data and code to reproduce the "Freezing and Shielding under Global Quenches for Many-Body Systems with Long-Range Couplings" data in https://arxiv.org/abs/2407.06072. The mathematica file just perform a numerical integral that computes the double occupaciens with second order unitary perturbation theory for a semi-circular density of states of the unperturbed state. The python files also compute double occupaciens with second order unitary perturbation theory for a finite system where the density of states cannot be approximated by a continuous functions but it is just a collection of eigenenergies. The Fig1.ipynb file computes the dynamics of three local excitations for the spin model and the Fermi-Hubbard model with off-diagonal disorder and long-range hopping/interactions. Ther is a python file that computes the fidelity decay.