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

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 speed up 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 simulating 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 (qMCMC) algorithm on Quantinuum System Model H2 and Quantinuum Helios quantum computers. We first demonstrate that it is possible to obtain accurate results by operating directly on the physical qubits. Crucially, to pave the way toward fault-tolerant execution, we also implement these algorithms using logical qubits protected by the Iceberg Quantum Error Detection (QED) code. By applying multiple rounds of mid-circuit QED during a random walk, we successfully catch and filter out hardware errors. These experiments demonstrate the feasibility of qMCMC on quantum hardware, bringing us closer to realizing quadratic quantum speedups with broad applications ranging from molecular modeling to machine learning and finance.

arXiv:2603.08395 [quant-ph]

(or arXiv:2603.08395v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.08395 Focus to learn more arXiv-issued DOI via DataCite

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