Enabling Quantum Speedup of Markov Chains using a Multi-level Approach
Quantum Physics
2022-10-26 v1 Numerical Analysis
Numerical Analysis
Abstract
Quantum speedup for mixing a Markov chain can be achieved based on the construction of slowly-varying Markov chains where the initial chain can be easily prepared and the spectral gaps have uniform lower bound. The overall complexity is proportional to . We present a multi-level approach to construct such a sequence of Markov chains by varying a resolution parameter We show that the density function of a low-resolution Markov chain can be used to warm start the Markov chain with high resolution. We prove that in terms of the chain length the new algorithm has complexity rather than
Cite
@article{arxiv.2210.14088,
title = {Enabling Quantum Speedup of Markov Chains using a Multi-level Approach},
author = {Xiantao Li},
journal= {arXiv preprint arXiv:2210.14088},
year = {2022}
}