Probing spectral features of quantum many-body systems with quantum simulators

TL;DR

This paper introduces a quantum simulation framework for efficiently probing the spectral features of quantum many-body systems, leveraging native Hamiltonian evolution and engineered frequency resonance, with robustness to noise and practical experimental demonstrations.

Contribution

The work presents a novel spectral probing method that requires no ancilla, achieves logarithmic time complexity for energy estimation, and demonstrates scalability and noise robustness in quantum simulators.

Findings

Spectral features can be efficiently probed with polynomial time complexity.

The method is robust to noise and scalable to larger systems.

Experimental demonstrations on IBM quantum devices validate the approach.

Abstract

The efficient probing of spectral features is important for characterising and understanding the structure and dynamics of quantum materials. In this work, we establish a framework for probing the excitation spectrum of quantum many-body systems with quantum simulators. Our approach effectively realises a spectral detector by processing the dynamics of observables with time intervals drawn from a defined probability distribution, which only requires native time evolution governed by the Hamiltonian without ancilla. The critical element of our method is the engineered emergence of frequency resonance such that the excitation spectrum can be probed. We show that the time complexity for transition energy estimation has a logarithmic dependence on simulation accuracy and how such observation can be guaranteed in certain many-body systems. We discuss the noise robustness of our spectroscopic method and show that the total running time maintains polynomial dependence on accuracy in the presence of device noise. We further numerically test the error dependence and the scalability of our method for lattice models. We present simulation results for the spectral features of typical quantum systems, either gapped or gapless, including quantum spins, fermions and bosons. We demonstrate how excitation spectra of spin-lattice models can be probed experimentally with IBM quantum devices.