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arXiv · 2603.11197

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

Xiantao Li
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Abstract

We present near-term quantum algorithms for auxiliary-field quantum Monte Carlo (AFQMC), viewed as imaginary-time projection for ground-state calculation as an ensemble of one-body propagators driven by stochastic fields $\Omega$. 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 $\|\Omega \| \tau=O(1)$ 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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Xiantao Li. 2026-03-11. Auxiliary-Field Quantum Monte Carlo on Quantum Hardware via Unitary Dilation. https://arxiv.org/abs/2603.11197

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