Bell sampling in Quantum Monte Carlo simulations

TL;DR

Bell-QMC introduces a novel quantum Monte Carlo framework using Bell sampling, enabling efficient and unbiased estimation of challenging observables and entanglement, thus broadening the scope of quantum properties accessible in simulations.

Contribution

This work presents Bell-QMC, a new QMC approach leveraging Bell sampling to efficiently estimate off-diagonal operators and entanglement, surpassing previous methods.

Findings

Bell-QMC accurately estimates off-diagonal observables.

Entanglement across all partitions can be computed in a single simulation.

The method is effective in models like the transverse-field Ising and Z2 lattice gauge theory.

Abstract

Quantum Monte Carlo (QMC) methods are essential for the numerical study of large-scale quantum many-body systems, yet their utility has been significantly hampered by the difficulty in computing key quantities such as off-diagonal operators and entanglement. This work introduces Bell-QMC, a novel QMC framework leveraging Bell sampling, a two-copy measurement protocol in the transversal Bell basis. We demonstrate that Bell-QMC enables an efficient and unbiased estimation of both challenging classes of observables, offering a significant advantage over previous QMC approaches. Notably, the entanglement across all system partitions can be computed in a single Bell-QMC simulation. We implement this method within the stochastic series expansion (SSE), where we design an efficient update scheme for sampling the configurations in the Bell basis. We demonstrate our algorithm in the one-dimensional transverse-field Ising model and the two-dimensional $\mathbb{Z}_2$ lattice gauge theory, extracting universal quantum features using only simple diagonal measurements. This work establishes Bell-QMC as a powerful framework that significantly expands the accessible quantum properties in QMC simulations, providing a substantial advantage over conventional QMC.