Noise-Robust Detection of Quantum Phase Transitions

TL;DR

This paper demonstrates that certain observables like energy derivatives and correlation functions can reliably detect quantum phase transitions on noisy quantum hardware, reducing the need for extensive error mitigation.

Contribution

It introduces a noise-robust approach to identify quantum phase transitions using simple measurements that are less affected by hardware noise.

Findings

Energy derivative and correlation functions are reliable indicators of phase transitions.

Minimal error mitigation is needed for accurate detection of phase transitions.

Method is applicable to near-term quantum devices for studying complex quantum phenomena.

Abstract

Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the study of ground-states of condensed matter models, and the transitions between them. However, current levels of hardware noise can require extensive application of error-mitigation techniques to achieve reliable computations. In this work, we use several IBM devices to explore a finite-size spin model with multiple `phase-like' regions characterized by distinct ground-state configurations. Using pre-optimized Variational Quantum Eigensolver (VQE) solutions, we demonstrate that in contrast to calculating the energy, where zero-noise extrapolation is required in order to obtain qualitatively accurate yet still unreliable results, calculations of the energy derivative, two-site spin correlation functions, and the fidelity susceptibility yield accurate behavior across multiple regions, even with minimal or no application of error-mitigation approaches. Taken together, these sets of observables could be used to identify level crossings in a simple, noise-robust manner which is agnostic to the method of ground state preparation. This work shows promising potential for near-term application to identifying quantum phase transitions, including avoided crossings and non-adiabatic conical intersections in electronic structure calculations.