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arXiv · 2603.22422

Preparing Fermions via Classical Sampling and Linear Combinations of Unitaries

Erik J. Gustafson·Henry Lamm
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Abstract

We present an extension of the Evolving density matrices on Qubits (E$\rho$OQ) framework that enables efficient fault-tolerant preparation of fermionic quantum states. The original method circumvents state preparation by stochastic sampling, but faces a sign problem in fermionic systems leading to a large number of circuits necessary. We resolve this by combining classical stochastic sampling with a linear combination of unitaries method that avoids the exponential circuit scaling that plagued na\"{i}ve implementations. The resulting algorithm requires $\mathcal{O}(M^2)$ $R_Z$ rotations for circuit preparation, where $M$ is the number of retained basis states. We validate the method for ground and excited states in the Thirring model, including by computing two-point correlation functions relevant to scattering. In this model for fixed accuracy $\varepsilon$, $M$ is found to scale empirically as $M \propto \frac{1}{mg}\log(1/g)\log(1/m)$.

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Erik J. Gustafson, Henry Lamm. 2026-03-23. Preparing Fermions via Classical Sampling and Linear Combinations of Unitaries. https://arxiv.org/abs/2603.22422

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