Method and system for quantum sampling in nonreversible markov chains using quantum technics

Abstract

The invention relates to methods and systems for operating a quantum computing device to sample from an approximate stationary distribution of a Markov chain P having n states, through the construction and execution of a quantum circuit, said method comprising the step of: Initialize an ancilla qubit to the ∣0> state and at least one qubit register in its initial state; Prepare an unitary matrix U, which encodes a discriminant D in block form, allowing polynomial transformations of its singular values or eigenvalues; Apply successively a single qubit gate on the ancilla qubit and the ancilla controlled unitary matrix U on the qubit registers creating a reflection about an approximation of the stationary distribution of the Markov Chain P; and Prepare an approximation of the sought coherent quantum state associated with the stationary distribution, preferably using quantum amplitude amplification

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