General scope of quantum Monte Carlo extensions for many-body quantum information

Determine how far quantum Monte Carlo extensions to nonlinear many-body quantum-information diagnostics can be developed while preserving the principal strengths of quantum Monte Carlo.

Background

The review surveys quantum Monte Carlo formulations for accessing observables and state constructions that go beyond conventional linear expectation values, including Rényi entropies, Rényi negativities, stabilizer entropies, reduced density matrices, replicated states, and decohered density matrices. These extensions rely on specialized replica constructions, generalized partition-function ratios, basis choices, operator insertions, and quantum-channel representations.

The authors identify a broad unresolved methodological question: whether these increasingly general constructions can retain the scalability, controllability, and sign-problem-free sampling advantages that motivate quantum Monte Carlo. Because different formulations have substantially different computational properties, the review does not provide a complete answer.

References

A central question is how far these extensions can be developed while preserving the main strengths of QMC. A complete answer is not yet available, partly because different QMC formulations can differ substantially.

— Quantum Monte Carlo in the Age of Many-Body Quantum Information  (2608.23231 - Ding et al., 24 Aug 2026) in Section 1, Introduction

We further note that, while a solution of the Kitaev honeycomb model in terms of a Jordan–Wigner transformation is available, the procedure involves the decoupling of a quartic term, which again introduces a gauge redundancy . It is therefore not obvious whether or how this or other solution schemes can enable an efficient sampling routine for the SRE~eq:sre.

— Magic of Kitaev spin liquids  (2608.25929 - Lamma et al., 26 Aug 2026) in Section 2, subsection “Evaluation of Pauli strings”