Term Grouping and Travelling Salesperson for Digital Quantum Simulation

TL;DR

This paper introduces a novel term grouping and ordering strategy, max-commute-tsp, to improve quantum simulation fidelity and reduce gate counts by mitigating errors and optimizing circuit design for near-term quantum devices.

Contribution

It proposes the max-commute-tsp method for term ordering and gate cancellation, enhancing quantum simulation accuracy and efficiency on noisy, limited-capability quantum hardware.

Findings

Improved Trotter fidelity through term reordering and partitioning.

Effective gate count reduction via TSP-based gate cancellation.

Demonstrated robustness of methods under realistic noise models.

Abstract

Digital simulation of quantum dynamics by evaluating the time evolution of a Hamiltonian is the initially proposed application of quantum computing. The large number of quantum gates required for emulating the complete second quantization form of the Hamiltonian, however, makes such an approach unsuitable for near-term devices with limited gate fidelities that cause high physical errors. In addition, Trotter error caused by noncommuting terms can accumulate and harm the overall circuit fidelity, thus causing algorithmic errors. In this paper, we propose a new term ordering strategy, max-commute-tsp (MCTSP), that simultaneously mitigates both algorithmic and physical errors. First, we improve the Trotter fidelity compared with previously proposed optimization by reordering Pauli terms and partitioning them into commuting families. We demonstrate the practicality of this method by constructing and evaluating quantum circuits that simulate different molecular Hamiltonians, together with theoretical explanations for the fidelity improvements from our term grouping method. Second, we describe a new gate cancellation technique that reduces the high gate counts by formulating the gate cancellation problem as a travelling salesperson problem, together with benchmarking experiments. Finally, we also provide benchmarking results that demonstrate the combined advantage of max-commute-tsp to mitigate both physical and algorithmic errors via quantum circuit simulation under realistic noise models.