GFlowNets for Hamiltonian decomposition in groups of compatible operators

TL;DR

This paper introduces a probabilistic GFlowNet-based method to optimize grouping of Hamiltonian terms, significantly reducing measurements needed in quantum simulations and offering versatile applications in resource management.

Contribution

It presents a novel GFlowNet framework for grouping commuting Hamiltonian terms, outperforming greedy algorithms in measurement reduction and adaptable to other quantum resource optimization tasks.

Findings

51% reduction in measurements for FC groupings

67% reduction in measurements for QWC groupings

Demonstrates GFlowNets' potential in quantum resource optimization

Abstract

Quantum computing presents a promising alternative for the direct simulation of quantum systems with the potential to explore chemical problems beyond the capabilities of classical methods. However, current quantum algorithms are constrained by hardware limitations and the increased number of measurements required to achieve chemical accuracy. To address the measurement challenge, techniques for grouping commuting and anti-commuting terms, driven by heuristics, have been developed to reduce the number of measurements needed in quantum algorithms on near-term quantum devices. In this work, we propose a probabilistic framework using GFlowNets to group fully (FC) or qubit-wise commuting (QWC) terms within a given Hamiltonian. The significance of this approach is demonstrated by the reduced number of measurements for the found groupings; 51% and 67% reduction factors respectively for FC and QWC partitionings with respect to greedy coloring algorithms, highlighting the potential of GFlowNets for future applications in the measurement problem. Furthermore, the flexibility of our algorithm extends its applicability to other resource optimization problems in Hamiltonian simulation, such as circuit design.