PreprintCC BY 4.0arXiv
A Simple Quantum Linear-System Solver via Dissipation
Abstract
Dissipation has been recently demonstrated as a powerful primitive for designing quantum algorithms. We apply this viewpoint directly to linear-system solving, Ax=b. We construct a simple purely dissipative Lindbladian whose unique fixed point encodes the linear-system solution. We prove dimension-independent trace-distance mixing in Θ(κ2log(1/eps)) time. We then show how to run this Lindbladian on digital quantum computers via collective block encoding and Lindbladian simulation, resulting in an O (κ2log(1/eps) log(κ/eps)/loglog(κ/eps)) query complexity for both UA, the block encoding of A, and Ub, the |b⟩ state preparation unitary.
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BibTeX
@misc{shang2026simple,
title = {{A Simple Quantum Linear-System Solver via Dissipation}},
author = {Zhong-Xia Shang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12284},
eprint = {2609.12284},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12284},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Simple Quantum Linear-System Solver via Dissipation
AU - Zhong-Xia Shang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12284
UR - https://arxiv.org/abs/2609.12284
AB - Dissipation has been recently demonstrated as a powerful primitive for designing quantum algorithms. We apply this viewpoint directly to linear-system solving, Ax=b. We construct a simple purely dissipative Lindbladian whose unique fixed point encodes the linear-system solution. We prove dimension-independent trace-distance mixing in Θ(κ^2log(1/eps)) time. We then show how to run this Lindbladian on digital quantum computers via collective block encoding and Lindbladian simulation, resulting in an O (κ^2log(1/eps) log(κ/eps)/loglog(κ/eps)) query complexity for both U_A, the block encoding of A, and U_b, the |b⟩ state preparation unitary.
ER -