Auxiliary-Field Quantum Monte Carlo on Quantum Hardware via Unitary Dilation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910083764453376 |
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| author | Li, Xiantao |
| author_facet | Li, Xiantao |
| contents | 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 $Ω$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11197 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Auxiliary-Field Quantum Monte Carlo on Quantum Hardware via Unitary Dilation Li, Xiantao Quantum Physics 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 $Ω$. 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. |
| title | Auxiliary-Field Quantum Monte Carlo on Quantum Hardware via Unitary Dilation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.11197 |