Determinant Quantum-Quantum Monte Carlo: Coherent Auxiliary-Field Sampling
Abstract
We introduce determinant quantum-quantum Monte Carlo (DQ2MC), a quantum algorithm that lifts the auxiliary-field sampling and averaging at the operational core of determinant quantum Monte Carlo onto a quantum computer. A determinant oracle synthesizes the DQMC amplitudes directly from a block encoding of the single-particle action matrix via quantum singular value transformations, so that the exponentially many Hubbard-Stratonovich weights are never enumerated, precomputed, or stored. Since the fermions are free for fixed auxiliary fields, the construction operates entirely at the single-particle level, requiring O(log Nst) system qubits and no Jordan-Wigner or Bravyi-Kitaev encoding, where Nst is the space-time volume. A full-quantum protocol makes observables interference amplitudes, eliminating the Markov chain and its autocorrelation time altogether; a hybrid quantum-classical protocol retains a constant-size active block of qubits and replaces the Metropolis-Hastings acceptance step with an exact heat-bath draw, so that cluster updates of any size are rejection-free, and passes only classical information between updates, admitting parallel tempering and distributed execution across quantum processors. The circuit-depth scales more favorably with spatial volume than classical DQMC, at the price of a post-selection overhead determined exactly by the largest target probability --- polynomial for smooth distributions, exponential for sharply peaked ones. Finally, the reweighting estimator underlying the fermion sign problem maps exactly onto a quantum weak value, placing the exponential cost of sign-problematic DQMC in precise correspondence with the post-selection overhead of weak-value extraction.
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BibTeX
@misc{wang2026determinant,
title = {{Determinant Quantum-Quantum Monte Carlo: Coherent Auxiliary-Field Sampling}},
author = {Xuepeng Wang and Sagnik Banerjee and Debanjan Chowdhury},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28742},
eprint = {2608.28742},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28742},
}
RIS
TY - UNPB
TI - Determinant Quantum-Quantum Monte Carlo: Coherent Auxiliary-Field Sampling
AU - Xuepeng Wang
AU - Sagnik Banerjee
AU - Debanjan Chowdhury
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28742
UR - https://arxiv.org/abs/2608.28742
AB - We introduce determinant quantum-quantum Monte Carlo (DQ^2MC), a quantum algorithm that lifts the auxiliary-field sampling and averaging at the operational core of determinant quantum Monte Carlo onto a quantum computer. A determinant oracle synthesizes the DQMC amplitudes directly from a block encoding of the single-particle action matrix via quantum singular value transformations, so that the exponentially many Hubbard-Stratonovich weights are never enumerated, precomputed, or stored. Since the fermions are free for fixed auxiliary fields, the construction operates entirely at the single-particle level, requiring O(log N_st) system qubits and no Jordan-Wigner or Bravyi-Kitaev encoding, where N_st is the space-time volume. A full-quantum protocol makes observables interference amplitudes, eliminating the Markov chain and its autocorrelation time altogether; a hybrid quantum-classical protocol retains a constant-size active block of qubits and replaces the Metropolis-Hastings acceptance step with an exact heat-bath draw, so that cluster updates of any size are rejection-free, and passes only classical information between updates, admitting parallel tempering and distributed execution across quantum processors. The circuit-depth scales more favorably with spatial volume than classical DQMC, at the price of a post-selection overhead determined exactly by the largest target probability --- polynomial for smooth distributions, exponential for sharply peaked ones. Finally, the reweighting estimator underlying the fermion sign problem maps exactly onto a quantum weak value, placing the exponential cost of sign-problematic DQMC in precise correspondence with the post-selection overhead of weak-value extraction.
ER -