Quantized Markov Chain Couplings that Prepare Qsamples

Fuente: arXiv
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Main Authors: Temme, Kristan, Wocjan, Pawel
Format: Preprint
Published: 2025
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author Temme, Kristan
Wocjan, Pawel
author_facet Temme, Kristan
Wocjan, Pawel
contents We present a novel approach to quantizing Markov chains. The approach is based on the Markov chain coupling method, which is frequently used to prove fast mixing. Given a particular coupling, e.g., a grand coupling, we construct a completely positive and trace preserving map. This quantum map has a unique fixed point, which corresponds to the quantum sample (qsample) of the classical Markov chain's stationary distribution. We show that the convergence time of the quantum map is directly related to the coupling time of the Markov chain coupling.
format Preprint
id arxiv_https___arxiv_org_abs_2504_02651
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quantized Markov Chain Couplings that Prepare Qsamples
Temme, Kristan
Wocjan, Pawel
Quantum Physics
Mathematical Physics
We present a novel approach to quantizing Markov chains. The approach is based on the Markov chain coupling method, which is frequently used to prove fast mixing. Given a particular coupling, e.g., a grand coupling, we construct a completely positive and trace preserving map. This quantum map has a unique fixed point, which corresponds to the quantum sample (qsample) of the classical Markov chain's stationary distribution. We show that the convergence time of the quantum map is directly related to the coupling time of the Markov chain coupling.
title Quantized Markov Chain Couplings that Prepare Qsamples
topic Quantum Physics
Mathematical Physics
url https://arxiv.org/abs/2504.02651