Experimental Realization of the Markov Chain Monte Carlo Algorithm on a Quantum Computer

TL;DR

This paper demonstrates the experimental implementation of a quantum Markov Chain Monte Carlo algorithm on NISQ hardware, showing promising results for quantum sampling tasks with current quantum computers.

Contribution

It is the first experimental realization of qMCMC on actual quantum hardware, utilizing encodings of Markov chains on NISQ devices.

Findings

Accurate results obtained on Quantinuum's H2 and Helios quantum computers.

Quantum Markov Chain Monte Carlo feasible on current NISQ hardware.

Shows potential for quantum advantage in sampling tasks.

Abstract

Quantum algorithms present a quadratically improved complexity over classical ones for certain sampling tasks. For instance, the Quantum Amplitude Estimation (QAE) algorithm promises to speedup the estimation of the mean of certain functions, given access to the quantum state corresponding to the probability distribution to be sampled from. Classically, samples are often obtained by running steps a Markov Chain. In this work, we experimentally use encodings of Markov chains to prepare quantum states and run a quantum Markov Chain Monte Carlo algorithm (qMCMC) on Quantinuum's H2 and Helios quantum computers. We demonstrate that it is possible to obtain accurate results on current Noisy Intermediate Scale Quantum (NISQ) hardware, operating directly on the physical qubits.