Double-bracket quantum algorithms for high-fidelity ground state preparation

TL;DR

This paper introduces double-bracket quantum algorithms (DBQAs) that improve ground state preparation fidelity on near-term quantum devices by refining initial circuits, demonstrated through experiments and simulations on IBM and Quantinuum hardware.

Contribution

The paper proposes a practical strategy for implementing DBQAs to enhance ground state preparation, including compilation for Heisenberg chains and experimental validation on real quantum hardware.

Findings

DBQAs improve energy and fidelity over initial states.

Experimental results show significant improvement with error mitigation.

Simulations suggest hardware execution can achieve similar gains without error mitigation.

Abstract

Ground state preparation is a central application for quantum computers but remains challenging in practice. In this work, we quantitatively investigate the performance and gate counts of double-bracket quantum algorithms (DBQAs) for ground state preparation. We propose a practical strategy in which DBQAs refine initial state preparation circuits, and we compile them for Heisenberg chains using controlled-Z and single-qubit gates. Warm-started DBQAs consistently improve both the energy and ground-state fidelity relative to the initial states provided by variational ans\"atze, indicating that DBQAs offer an effective unitary synthesis method. To demonstrate compatibility with near-term hardware, we executed a proof-of-concept example on IBM devices. With error mitigation, we observed a statistically significant improvement over the corresponding warm-start circuit. Furthermore, numerical emulations for the same system size indicate that executing DBQAs on Quantinuum's hardware could achieve similar cost-function gains without requiring error mitigation. These findings suggest that DBQAs are a promising approach for enhancing ground-state approximations on near-term quantum devices.