Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows

Abstract

Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry and condensed matter physics. The rapid emergence and development of quantum computers offer a promising route to systematically tackle this problem. Recent work by Huggins et al.[1] proposed a hybrid quantum-classical quantum Monte Carlo (QC-QMC) algorithm using Clifford shadows to determine the ground state of a Fermionic Hamiltonian. This approach displayed inherent noise resilience and the potential for improved accuracy compared to its purely classical counterpart. Nevertheless, the use of Clifford shadows introduces an exponentially scaling post-processing cost. In this work, we investigate an improved QC-QMC scheme utilizing the recently developed Matchgate shadows technique [2], which removes the aforementioned exponential bottleneck. We observe from experiments on quantum hardware that the use of Matchgate shadows in QC-QMC is inherently noise robust. We show that this noise resilience has a more subtle origin than in the case of Clifford shadows. Nevertheless, we find that classical post-processing, while asymptotically efficient, requires hours of runtime on thousands of classical CPUs for even the smallest chemical systems, presenting a major challenge to the scalability of the algorithm.

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Cited by in corpus (8)

• Unbiasing Fermionic Auxiliary-Field Quantum Monte Carlo with Matrix Product State Trial Wavefunctions
• Improved modularity and new features in ipie: Toward even larger AFQMC calculations on CPUs and GPUs at zero and finite temperatures
• Implementing advanced trial wave functions in fermion quantum Monte Carlo via stochastic sampling
• A quantum computing approach to fixed-node Monte Carlo using classical shadows
• Quantum-Classical Auxiliary Field Quantum Monte Carlo with Matchgate Shadows on Trapped Ion Quantum Computers
• Classical Shadows with Improved Median-of-Means Estimation
• Enhancing quantum computations with the synergy of auxiliary field quantum Monte Carlo and computational basis tomography
• Constrained Shadow Tomography for Molecular Simulation on Quantum Devices