Low-Resource Quantum Energy Gap Estimation via Randomization

TL;DR

This paper introduces a hybrid quantum-classical method called TE-PAI shadow spectroscopy that efficiently estimates energy gaps in quantum systems using shallow circuits, improving noise robustness and suitability for NISQ devices.

Contribution

It develops a novel hybrid protocol integrating TE-PAI with shadow spectroscopy, enabling accurate spectral estimation with low-depth circuits on noisy quantum hardware.

Findings

Accurately resolves energy gaps in simulations.

Demonstrates robustness to gate noise.

Successfully implemented on 20-qubit IBM hardware.

Abstract

Estimating the energy spectra of quantum many-body systems is a fundamental task in quantum physics, with applications ranging from chemistry to condensed matter. Algorithmic shadow spectroscopy is a recent method that leverages randomized measurements on time-evolved quantum states to extract spectral information. However, implementing accurate time evolution with low-depth circuits remains a key challenge for near-term quantum hardware. In this work, we propose a hybrid quantum-classical protocol that integrates Time Evolution via Probabilistic Angle Interpolation (TE-PAI) into the shadow spectroscopy framework. TE-PAI enables the simulation of time evolution using shallow stochastic circuits while preserving unbiased estimates through quasiprobability sampling. We construct the combined estimator and derive its theoretical properties. Through numerical simulations, we demonstrate that our method accurately resolves energy gaps and exhibits enhanced robustness to gate noise compared to standard Trotter-based shadow spectroscopy. We further validate the protocol experimentally on up to 20 qubits using IBM quantum hardware. This makes TE-PAI shadow spectroscopy a promising tool for spectral analysis on noisy intermediate-scale quantum (NISQ) devices.