Resilience of scrambling measurements

Abstract

Most experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backward time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

Probing out-of-time-order correlators

“…It would be interesting to extend the currently existing OTOC measurement protocols [3,4,14,15,[37][38][39] to this context. The effective action described in this work might also be relevant in describing decoherence in the context of weak measurements [40][41][42][43][44].…”

Strengthening weak measurements of qubit out-of-time-order correlators

“…Such observables can have only two distinct subspaces, associated with the eigenvalues ±1, and so are natural observables to consider for practical circuit simulations using qubits. For example, the OTOC for two single-qubit observables that lie at opposite ends of a spin chain undergoing nonintegrable dynamics would be a natural shortterm experimental goal [31,35,36,[47][48][49].…”

Verified quantum information scrambling

“…For example, non-unitary timeevolution arising from depolarization or classical noise processes naturally lead the OTOC to decay, even in the absence of quantum scrambling. A similar decay can also originate from even slight mismatches between the purported forward and backwards time-evolution ofŴ (t) [7,19,28]. While full quantum tomography can in principle distinguish scrambling from decoherence and experimental noise, this requires a number of measurements that scales exponentially with system size and is thus impractical.…”