Quantum impurity models: easy at equilibrium, universal in motion
Abstract
A quantum impurity model describes a small interacting subsystem embedded into a large bath of free fermions. Here we study the computational complexity of calculating the ground energy, thermal equilibrium, and dynamical properties of these models. Our work reveals a sharp contrast: equilibrium properties can be efficiently approximated by classical means, whereas time evolution can implement a universal quantum computation. More precisely, let H be the Hamiltonian of an impurity model with n fermionic modes and a constant-size impurity. We show that: (1) the ground energy of H can be approximated to additive error ε by a classical algorithm with runtime textsfpoly(n,1/ε), improving on the quasi-polynomial runtime of the best previously known algorithm; (2) at inverse temperature β, the Helmholtz free energy and a classical description of the thermofield double state can be computed to precision ε in time textsfpoly(n,β,1/ε); (3) simulating the time evolution e−iHt is textsfBQP-complete, for H that is time-independent and has a fixed, constant impurity size. Our algorithms exploit exponential suppression of multi-particle bath excitations in a basis organized by energy scale and Krylov depth. Our universality construction realizes a stationary quantum processor whose program arrives in a stream of freely propagating fermions.
Related
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BibTeX
@misc{arunachalam2026quantum,
title = {{Quantum impurity models: easy at equilibrium, universal in motion}},
author = {Srinivasan Arunachalam and Sergey Bravyi and Anirban Chowdhury and Arkopal Dutt and Alexandru Gheorghiu and Zhi Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02130},
eprint = {2610.02130},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02130},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum impurity models: easy at equilibrium, universal in motion
AU - Srinivasan Arunachalam
AU - Sergey Bravyi
AU - Anirban Chowdhury
AU - Arkopal Dutt
AU - Alexandru Gheorghiu
AU - Zhi Li
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02130
UR - https://arxiv.org/abs/2610.02130
AB - A quantum impurity model describes a small interacting subsystem embedded into a large bath of free fermions. Here we study the computational complexity of calculating the ground energy, thermal equilibrium, and dynamical properties of these models. Our work reveals a sharp contrast: equilibrium properties can be efficiently approximated by classical means, whereas time evolution can implement a universal quantum computation. More precisely, let H be the Hamiltonian of an impurity model with n fermionic modes and a constant-size impurity. We show that: (1) the ground energy of H can be approximated to additive error ε by a classical algorithm with runtime textsfpoly(n,1/ε), improving on the quasi-polynomial runtime of the best previously known algorithm; (2) at inverse temperature β, the Helmholtz free energy and a classical description of the thermofield double state can be computed to precision ε in time textsfpoly(n,β,1/ε); (3) simulating the time evolution e^−iHt is textsfBQP-complete, for H that is time-independent and has a fixed, constant impurity size. Our algorithms exploit exponential suppression of multi-particle bath excitations in a basis organized by energy scale and Krylov depth. Our universality construction realizes a stationary quantum processor whose program arrives in a stream of freely propagating fermions.
ER -