Effect of noise on quantum circuit realization of non-Hermitian time crystals

TL;DR

This paper investigates how noise affects the realization of non-Hermitian time crystals on noisy quantum computers, showing that ideal persistent oscillations are generally damped by noise, with experimental limitations observed on real devices.

Contribution

It demonstrates the impact of noise on non-Hermitian time crystal dynamics and provides a detailed analysis of damping effects using simulations and experiments.

Findings

Persistent oscillations are long-lived in ideal non-Hermitian dynamics.

Noise causes damping and eventual loss of oscillations.

Real device experiments do not show persistent oscillations due to noise.

Abstract

Non-Hermitian quantum dynamics lie in an intermediate regime between unitary Hamiltonian dynamics and trace-preserving non-unitary open quantum system dynamics. Given differences in the noise tolerance of unitary and non-unitary dynamics, it is interesting to consider implementing non-Hermitian dynamics on a noisy quantum computer. In this paper, we do so for a non-Hermitian Ising Floquet model whose many-body dynamics gives rise to persistent temporal oscillations, a form of time crystallinity. In the simplest two qubit case that we consider, there is an infinitely long-lived periodic steady state at certain fine-tuned points. These oscillations remain reasonably long-lived over a range of parameters in the ideal non-Hermitean dynamics and for the levels of noise and imperfection expected of modern day quantum devices. Using a generalized Floquet analysis, we show that infinitely long-lived oscillations are generically lost for arbitrarily weak values of common types of noise and compute corresponding damping rate. We perform simulations using IBM's Qiskit platform to confirm our findings; however, experiments on a real device (ibmq-lima) do not show remnants of these oscillations.