On Quantum Algorithms for Efficient Solutions of General Classes of Structured Markov Processes
arxiv(2024)
摘要
We study the fundamental problem of efficiently computing the stationary
distribution of general classes of structured Markov processes. In strong
contrast with previous work, we consider this problem within the context of
quantum computational environments from a mathematical perspective and devise
the first quantum algorithms for computing the stationary distribution of
structured Markov processes. We derive a mathematical analysis of the
computational properties of our quantum algorithms together with related
theoretical results, establishing that our quantum algorithms provide the
potential for significant computational improvements over that of the
best-known classical algorithms in various settings of both theoretical and
practical importance. Although motivated by structured Markov processes, our
quantum algorithms have the potential for being exploited to address a much
larger class of numerical computation problems.
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