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 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.
Weihua Xie Michael Kolodrubetz Vadim Oganesyan