Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations

Abstract

In this work, the observation of the Lyapunov exponent in noisy quantum simulation experiments is shown to be bounded by three conditions that together make it presently out of reach. These conditions form a triangular region in parameter space with an area dependent on the number of qubits used. We predict that at least six qubits and 2.5 − 13x less error per CNOT gate on IBM-Q or 0.87 − 9.6x less error per Mølmer-Sørensen gate on IonQ are needed for the Lyapunov exponent to become experimentally observable. This prediction is achieved through close study of the quantum sawtooth map (QSM), which is the most efficiently simulated quantum system with a provably chaotic classical counterpart and rich dynamics.