Gibbs state preparation through quantum decoding
Abstract
We propose a Gibbs state preparation algorithm that exploits algebraic structure in the Hamiltonian. Our starting point is Hamiltonian Decoded Quantum Interferometry (HDQI), a recent algorithm that reduces Gibbs state preparation for Pauli Hamiltonians to decoding error-correcting codes. We introduce quantum decoding HDQI (QD-HDQI), replacing HDQI's coherent classical decoder by a quantum decoder that can exploit interference between different errors. For commuting Pauli Hamiltonians, our reduction is efficient and the associated quantum decoding problem corresponds to transmitting the associated symplectic code over i.i.d. pure-state classical-quantum channels. For uniformly random Hamiltonian signs, the vanishing-error threshold of an efficient decoder directly determines the lowest temperature that our algorithm can reach. Even using only classical decoders, this improves upon HDQI's achievable inverse temperature from linear to square-root in the correctable error fraction; quantum decoders can improve further by tolerating still stronger noise. A similar picture extends to the noncommuting regime previously handled by HDQI, where now the noise is correlated within small, independent blocks. We study two such quantum decoders in our QD-HDQI Gibbs sampling framework. The first, based on unambiguous state discrimination, works efficiently for arbitrary binary linear codes. However, we "dequantize" this strategy for commuting Hamiltonians, contributing a classical rejection sampler that matches its temperature threshold. The second is belief propagation with quantum messages (BPQM), a quantum generalization of classical belief propagation. We show that for certain dilute spin glasses, BPQM's decoding threshold exceeds the Shannon limit for classical decoding, reaching temperatures inaccessible to any classical decoder within our framework.
Related
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BibTeX
@misc{piveteau2026gibbs,
title = {{Gibbs state preparation through quantum decoding}},
author = {Christophe Piveteau and Yihui Quek and M. Isabel Franco Garrido},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03566},
eprint = {2610.03566},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03566},
}
RIS
TY - UNPB
TI - Gibbs state preparation through quantum decoding
AU - Christophe Piveteau
AU - Yihui Quek
AU - M. Isabel Franco Garrido
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03566
UR - https://arxiv.org/abs/2610.03566
AB - We propose a Gibbs state preparation algorithm that exploits algebraic structure in the Hamiltonian. Our starting point is Hamiltonian Decoded Quantum Interferometry (HDQI), a recent algorithm that reduces Gibbs state preparation for Pauli Hamiltonians to decoding error-correcting codes. We introduce quantum decoding HDQI (QD-HDQI), replacing HDQI's coherent classical decoder by a quantum decoder that can exploit interference between different errors. For commuting Pauli Hamiltonians, our reduction is efficient and the associated quantum decoding problem corresponds to transmitting the associated symplectic code over i.i.d. pure-state classical-quantum channels. For uniformly random Hamiltonian signs, the vanishing-error threshold of an efficient decoder directly determines the lowest temperature that our algorithm can reach. Even using only classical decoders, this improves upon HDQI's achievable inverse temperature from linear to square-root in the correctable error fraction; quantum decoders can improve further by tolerating still stronger noise. A similar picture extends to the noncommuting regime previously handled by HDQI, where now the noise is correlated within small, independent blocks. We study two such quantum decoders in our QD-HDQI Gibbs sampling framework. The first, based on unambiguous state discrimination, works efficiently for arbitrary binary linear codes. However, we "dequantize" this strategy for commuting Hamiltonians, contributing a classical rejection sampler that matches its temperature threshold. The second is belief propagation with quantum messages (BPQM), a quantum generalization of classical belief propagation. We show that for certain dilute spin glasses, BPQM's decoding threshold exceeds the Shannon limit for classical decoding, reaching temperatures inaccessible to any classical decoder within our framework.
ER -