Off-Diagonal Expansion Quantum Monte Carlo

Abstract

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a novel decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from `fully-quantum' to `fully-classical', in contrast to many existing methods. We demonstrate the advantages of the technique by comparing it against existing schemes. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

17 pages, 10 figures

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• Resolution of the Sign Problem for a Frustrated Triplet of Spins
• Permutation Matrix Representation Quantum Monte Carlo
• Calculating the divided differences of the exponential function by addition and removal of inputs
• Off-Diagonal Series Expansion for Quantum Partition Functions
• Rapid mixing of path integral Monte Carlo for 1D stoquastic Hamiltonians
• On the Question of Ergodicity in Quantum Spin Glass Phase and its role in Quantum Annealing
• An integral-free representation of the Dyson series using divided differences
• A quantum Monte Carlo algorithm for arbitrary spin-1/2 Hamiltonians
• A universal black-box quantum Monte Carlo approach to quantum phase transitions
• Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs
• Sampling and the complexity of nature
• Calculating elements of matrix functions using divided differences
• Quantum-Inspired Tempering for Ground State Approximation using Artificial Neural Networks
• A simple quantum simulation algorithm with near-optimal precision scaling
• A quantum Monte Carlo algorithm for arbitrary high-spin Hamiltonians
• Advanced measurement techniques in quantum Monte Carlo: The permutation matrix representation approach