Determinant Quantum-Quantum Monte Carlo: Coherent Auxiliary-Field Sampling

• URL: http://arxiv.org/abs/2608.28742v1
• Date: Fri, 28 Aug 2026 18:00:00 GMT
• Title: Determinant Quantum-Quantum Monte Carlo: Coherent Auxiliary-Field Sampling
• Abstract summary: We introduce quantum-quantum Monte Carlo (DQ$2$MC), a quantum algorithm that lifts the auxiliary-field sampling and averaging at the operational core of quantum Monte Carlo onto a quantum computer.<n>A full-quantum protocol makes observables interference amplitudes, eliminating the Markov chain and its autocorrelation time altogether.<n>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.
• Score: 1.263831889243274
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce determinant quantum-quantum Monte Carlo (DQ$^2$MC), 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 $O(\log N_{\mathrm{st}})$ system qubits and no Jordan-Wigner or Bravyi-Kitaev encoding, where $N_{\mathrm{st}}$ 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.

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