Quantum simulation of dynamical phase transitions in noisy quantum devices

TL;DR

This paper investigates the effects of noise on quantum simulations of dynamical phase transitions, showing how zero-noise extrapolation can both mitigate errors and reveal noise-induced phenomena.

Contribution

It introduces a matrix product density operator approach to analyze noisy quantum simulations of many-body dynamics, highlighting both limitations and advantages of zero-noise extrapolation.

Findings

Noise doubles the non-analytic points in the Loschmidt echo at phase transitions.

Zero-noise extrapolation can recover quantum revivals lost due to noise.

Results align with quantum simulator data, demonstrating the method's effectiveness.

Abstract

Zero-noise extrapolation provides an especially useful error mitigation method for noisy intermediate-scale quantum devices. Our analysis, based on matrix product density operators, of the transverse-field Ising model with depolarizing noise, reveals both advantages and inherent problems associated with zero-noise extrapolation when simulating non-equilibrium many-body dynamics. On the one hand, interestingly, noise alters systematically the behavior of the Loschmidt echo at the dynamical phase transition times, doubling the number of non-analytic points, and hence inducing an error that, inherently, cannot be mitigated. On the other, zero-noise extrapolation may be employed to recover quantum revivals of the Loschmidt echo, which would be completely missed in the absence of mitigation, and to retrieve faithfully noise-free inter-site correlations. Our results, which are in good agreement with those obtained using quantum simulators, reveal the potential of matrix product density operators for the investigation of the performance of quantum devices with a large number of qubits and deep noisy quantum circuits.