Noise-Resilient Trial-State Optimization Algorithm for Quantum Gap Estimation

Quantum simulation is believed one of the most promising avenues to reveal quantum advantage. Quantum phase estimation is a paradigm of unbiased quantum simulation but, in the original form, with high demand for deep circuits to tolerate errors. Hybrid quantum/classical algorithms such as variational methods were proposed as alternative approaches using shallow circuits on contemporary noisy quantum hardware while not offering a significant prospect for quantum advantage in scale up. In this work, we revisit the hybrid quantum gap estimation (QGE) algorithm [1] that combines Trotterized time evolution on a quantum processor with the classical fast Fourier transform of the damped time propagator to estimate the energy gaps of a many-body model to within a certain tolerance. We improve the accuracy of QGE by implementing trial-state unitaries with optimization parameters and using a classical optimizer to maximize the peak-to-background ratio in the many-body spectral function [2]. To verify performance, we demonstrate our algorithm for an example many-body model on the IBMQ simulator using device noise models. We prove that our algorithm is resilient against common mid-circuit Markovian noise channels, thus opening the door to a significant performance boost in scale up.