Quenched Thermodynamics from Ancilla-Assisted Imaginary-Time Evolution
Abstract
Quenched thermodynamics combines the equilibrium physics of fixed coupling configurations with a prescribed distribution of disorder. Problems related to quenched thermodynamics are generally intractable to approximate. We provide a quantum algorithm to calculate quenched disorder averages for the transverse-field Ising model, whose coupling configurations are organized into gauge classes. We show how to estimate these averages by preparing approximate Gibbs states through ancilla-assisted imaginary-time evolution. At each measurement, the ancilla record identifies the gauge class to which the energy estimate contributes. We validate our framework through an open 3×3 lattice. A one-step circuit resolves all sixteen flux classes, and a finite-shot calculation estimates the quenched energy for independently distributed bond signs. Thermodynamic integration extends the reconstruction to a quenched free-energy estimate, while comparison with exact diagonalization identifies the finite-step approximation as the dominant source of error. This use of the measurement record provides access to the thermodynamics of frustrated spin systems with a disorder distribution chosen independently of the circuit's sampling frequencies.
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BibTeX
@misc{adisa2026quenched,
title = {{Quenched Thermodynamics from Ancilla-Assisted Imaginary-Time Evolution}},
author = {Ibukunoluwa Adisa and Daniele Cuomo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38707},
eprint = {2610.38707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38707},
}
RIS
TY - UNPB
TI - Quenched Thermodynamics from Ancilla-Assisted Imaginary-Time Evolution
AU - Ibukunoluwa Adisa
AU - Daniele Cuomo
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38707
UR - https://arxiv.org/abs/2610.38707
AB - Quenched thermodynamics combines the equilibrium physics of fixed coupling configurations with a prescribed distribution of disorder. Problems related to quenched thermodynamics are generally intractable to approximate. We provide a quantum algorithm to calculate quenched disorder averages for the transverse-field Ising model, whose coupling configurations are organized into gauge classes. We show how to estimate these averages by preparing approximate Gibbs states through ancilla-assisted imaginary-time evolution. At each measurement, the ancilla record identifies the gauge class to which the energy estimate contributes. We validate our framework through an open 3×3 lattice. A one-step circuit resolves all sixteen flux classes, and a finite-shot calculation estimates the quenched energy for independently distributed bond signs. Thermodynamic integration extends the reconstruction to a quenched free-energy estimate, while comparison with exact diagonalization identifies the finite-step approximation as the dominant source of error. This use of the measurement record provides access to the thermodynamics of frustrated spin systems with a disorder distribution chosen independently of the circuit's sampling frequencies.
ER -