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

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 longlived periodic steady state at certain fine-tuned points. 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 the corresponding damping rate; this result is confirmed numerically using IBM's Qiskit platform. We further show that the complex gaps responsible for oscillation damping are opened generically at first order in perturbation theory for any convex combination of depolarization, relaxation, and dephasing, establishing that no engineered mixture of these noise channels can stabilize the time-crystalline phase. Experiments on a real device (ibmq-lima) are consistent with rapid oscillation damping, though a significant mismatch between the manufacturer noise model and observed device behavior complicates quantitative comparison, illustrating the importance of rigorous analytical noise analysis.