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

TL;DR

This paper develops quantum algorithms for auxiliary-field quantum Monte Carlo that convert nonunitary dynamics into unitary circuits, enabling more efficient ground-state simulations on quantum hardware.

Contribution

It introduces a method to embed nonunitary AFQMC slices into unitaries using stochastic Magnus expansions and LCU, reducing circuit depth and measurement overhead.

Findings

Classical benchmarks confirm the accuracy of the dilation and Magnus expansions.

Multi-step quantum circuit executions demonstrated on IBM hardware.

The approach enables coherent, shallow quantum circuits for ground-state calculations.

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.