Auxiliary-Field Quantum Monte Carlo on Quantum Hardware via Unitary Dilation

• URL: http://arxiv.org/abs/2603.11197v1
• Date: Wed, 11 Mar 2026 18:05:32 GMT
• Title: Auxiliary-Field Quantum Monte Carlo on Quantum Hardware via Unitary Dilation
• Abstract summary: We present near-term quantum algorithms for auxiliary-field quantum Monte Carlo (AFQMC)<n>We convert each trajectory into a sequence of piecewise-constant one-body generators using Magnus expansions up to second order.<n>This lifts the projector dynamics to a unitary evolution, enabling coherent circuit execution in the regime $|| =O$.
• Score: 3.3636842548621275
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present near-term quantum algorithms for auxiliary-field quantum Monte Carlo (AFQMC), which represents imaginary-time projection for ground-state calculation as an ensemble of one-body propagators driven by stochastic fields $Ω$. Starting from the Feynman-Kac formula, we convert each trajectory into a sequence of piecewise-constant one-body generators using stochastic Magnus expansions up to second order, and embed the resulting nonunitary slices into unitaries with a small ancilla overhead. This lifts the projector dynamics to a unitary evolution, enabling coherent circuit execution in the regime $\|Ω\| τ=O(1)$ and reducing the need for frequent mid-circuit measurement. We further derive an equivalent linear-combination-of-unitaries (LCU) form that yields system-only, shallower circuits by trading ancilla cost for additional trajectory sampling. Benchmarks on the Hubbard model verify the accuracy of the dilation and Magnus expansions classically and demonstrate multi-step executions on IBM quantum hardware.

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