Preparing Fermions via Classical Sampling and Linear Combinations of Unitaries

• URL: http://arxiv.org/abs/2603.22422v1
• Date: Mon, 23 Mar 2026 18:01:03 GMT
• Title: Preparing Fermions via Classical Sampling and Linear Combinations of Unitaries
• Abstract summary: We present an extension of the Evolving density matrices on Qubits (E$$OQ) framework that enables efficient fault-tolerant preparation of fermionic quantum states.<n>The original method circumvents state preparation by sampling, but faces a sign problem in fermionic systems leading to a large number of necessary circuits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an extension of the Evolving density matrices on Qubits (E$ρ$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 naïve 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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