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arXiv:2112.09083 · Physical review. D/Physical review. D.

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

Anthony N. Ciavarella, Ivan A. Chernyshev

Published Apr 19, 2022• 71 citations
arXivHTMLPDF

Abstract

Studying QCD and other gauge theories on quantum hardware requires the preparation of physically interesting states. The variational quantum eigensolver provides a way of performing vacuum state preparation on quantum hardware. In this work, variational quantum eigensolver 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. Small examples are performed on IBM's superconducting Manila processor.

DOI
10.1103/physrevd.105.074504

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The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm used to find the ground state of a Hamiltonian using variational methods. It has a wide range of potential applications, from quantum chemistry to lattice gauge theories in the Hamiltonian formulation. VQE relies on quantum computers to evaluate the energy of the system in terms of circuit parameters, and it minimizes this parametrized energy with a classical optimization routine. This work describes a Bayesian optimization (BO) algorithm specifically designed to minimize the parametrized energy obtained with a quantum computer. BO based on Gaussian process regression (GPR) is an algorithm for finding the global minimum of a black-box cost function, e.g. the energy, with a very low number of iterations even when using data affected by statistical noise. Furthermore, the GPR procedure developed for this work proved to be very versatile as we also used it to compute discrete integral transforms of noisy data. In particular, this procedure was used to reconstruct parton distribution functions from lattice QCD data.
Quantum-enhanced computing methods are promising candidates to solve currently intractable problems. We consider here a variational quantum eigensolver (VQE), that delegates costly state preparations and measurements to quantum hardware, while classical optimization techniques guide the quantum hardware to create a desired target state. In this work, we propose a bosonic VQE using superconducting microwave cavities, overcoming the typical restriction of a small Hilbert space when the VQE is qubit based. The considered platform allows for strong nonlinearities between photon modes, which are highly customisable and can be tuned in situ, i.e. during running experiments. Our proposal hence allows for the realization of a wide range of bosonic ansatz states, and is therefore especially useful when simulating models involving degrees of freedom that cannot be simply mapped to qubits, such as gauge theories, that include components which require infinite-dimensional Hilbert spaces. We thus propose to experimentally apply this bosonic VQE to the U(1) Higgs model including a topological term, which in general introduces a sign problem in the model, making it intractable with conventional Monte Carlo methods.
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