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arXiv · 2601.17732

Quantum fast-forwarding fermion-boson interactions via the polaron transform

Harriet Apel·Burak Şahinoğlu
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Abstract

Simulating interactions between fermions and bosons is central to understanding correlated phenomena, yet these systems are inherently difficult to treat classically. Previous quantum algorithms for fermion-boson models exhibit computation costs that scale polynomially with the bosonic truncation parameter, $\Lambda$. In this work we identify the efficient unitary transformation enabling fast-forwarded evolution of the fermion-boson interaction term, yielding an interaction-picture based simulation algorithm with complexity polylogarithmic in $\Lambda$. We apply this transformation to explicitly construct an efficient quantum algorithm for the Hubbard-Holstein model and discuss its generalisation to other fermion-boson interacting models. This approach yields an important asymptotic improvement in the dependence on the bosonic cutoff and establishes that, for certain models, fermion-boson interactions can be simulated with resources comparable to those required for purely fermionic systems.

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Harriet Apel, Burak Şahinoğlu. 2026-01-25. Quantum fast-forwarding fermion-boson interactions via the polaron transform. https://arxiv.org/abs/2601.17732

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