Researchers Run Quantum Markov Chains On Quantinuum Machine

A new study details a key step towards quantum-enhanced sampling methods. Baptiste Claudon from Qubit Pharmaceuticals, Sorbonne Universit é, LCT, UMR 7616 CNRS, and Sergi Ramos-Calderer from the Centre for Quantum Technologies, National University of Singapore, working with Jean-Philip Piquemal from Qubit Pharmaceuticals, Sorbonne Universit é, LCT, UMR 7616 CNRS, experimentally realised the Markov Chain Monte Carlo algorithm on Quantinuum’s H2 and Helios quantum computers. The research has demonstrated that accurate calculations are feasible on near-term quantum hardware by encoding Markov chains to prepare quantum states and running a quantum Markov Chain Monte Carlo algorithm, potentially offering substantial advantages over classical approaches for a range of applications.

Quantum algorithm achieves sharp error reduction on NISQ hardware via probabilistic encoding

Error rates dropped from approximately 3% to 0.6% when implementing the quantum Markov Chain Monte Carlo (qMCMC) algorithm on Quantinuum’s H2 and Helios quantum computers, crossing a threshold previously considered insurmountable for complex quantum subroutines. This reduction in error enabled the acquisition of accurate results directly on the physical qubits of Noisy Intermediate Scale Quantum (NISQ) hardware, something unattainable before due to the limitations of early prototype machines.

Quantum states were prepared using encodings of Markov chains and a quantum Markov Chain Monte Carlo algorithm was run on Quantinuum’s H2 and Helios quantum computers. Symmetric Projected Unitary Encoding (SPUE) embeds non-unitary operators into unitary operations, translating Markov chains—classical methods for generating random samples—into a quantum format.

Verification confirmed the resulting quantum state as an eigenvector. A Linear Combination of Unitaries approach and modifications of Szegedy’s method, a technique utilising the SWAP operator to encode the Markov chain’s spectral properties, were among the diverse encoding techniques deployed. These experiments were conducted on Quantinuum’s H2-1, H2-2, and Helios quantum computers, showing consistency across different hardware iterations.

Further analysis validated the process by confirming the quantum state produced was indeed an eigenvector of a second encoding method. While these results represent a major leap in accuracy, the current focus on two-state Markov chains limits immediate scalability to the far more complex systems required for real-world applications. This work serves as a foundational step towards simulating more complex systems, paving the way for future investigations into higher-dimensional Markov chains and their quantum representations.

Scaling qubit numbers remains central to realising practical quantum simulations

This breakthrough demonstrates the potential of noisy intermediate-scale quantum (NISQ) devices to tackle complex problems, but a significant hurdle remains: scaling. The algorithms used demand exponentially increasing resources as the complexity of the system being simulated grows, creating a bottleneck as maintaining qubit coherence and fidelity becomes increasingly difficult with each added qubit.

The team acknowledges this limitation, noting the current experiments are far from demonstrating a practical quantum advantage over classical methods for real-world applications. Obtaining accurate results directly on physical qubits—rather than relying on simulations—is a valuable step forward. It validates the underlying principles and techniques. Quantum algorithms offer a quadratically improved complexity over classical ones for certain sampling tasks.

The Quantum Amplitude Estimation (QAE) algorithm, for example, promises to speed up the estimation of the mean of functions, requiring access to the quantum state representing the probability distribution. Classical sampling often involves steps within a Markov Chain. A quantum Markov Chain Monte Carlo algorithm (qMCMC) was experimentally run on Quantinuum’s H2 and Helios quantum computers, demonstrating the possibility of obtaining accurate results on current Noisy Intermediate Scale Quantum (NISQ) hardware directly using physical qubits.

This demonstration opens questions regarding scaling these techniques to tackle increasingly intricate simulations and assessing the potential for quantum advantage over classical approaches, a distant but achievable goal. Successfully implementing a quantum Markov Chain Monte Carlo (qMCMC) algorithm on Quantinuum’s H2 and Helios processors confirms that accurate results are attainable with today’s Noisy Intermediate Scale Quantum (NISQ) technology.

Naren Manjunath from the Perimeter Institute and colleagues have established a pathway towards using near-term devices for complex computational tasks by encoding classical Markov chains—methods for generating random samples—into quantum states. This achievement validates the algorithms and techniques needed to explore more powerful quantum devices in the future, even if a practical advantage remains distant.

Error rates were significantly reduced. This moves beyond theoretical potential by directly operating on physical qubits, circumventing limitations previously imposed by error rates.