Southwest Quantum Information and Technology

Using chaotic quantum maps as a test of current quantum computing hardware fidelity*

Presenting Author: Max D. Porter, Laurence Livermore National Laboratory
Contributing Author(s): Ilon Joseph, Alessandro R. Castelli, Vasily Geyko, Frank R. Graziani, Stephen B. Libby, Yuan Shi, Jonathan L. DuBois

We explore the quantum simulation of chaotic dynamics on near term quantum computers using the quantum sawtooth map, the simplest quantum system with rich dynamics and a classically chaotic counterpart [G. Benenti, et al. Phys. Rev. Lett. 87, 227901-1 (2001)]. Depending on the parameters of the map, the competition between classical chaos and quantum interference can either produce diffusive chaotic dynamics or dynamical localization. The two regimes can be distinguished in the presence of noise by their fidelity, which decays exponentially in the chaotic case but only algebraically in the localized case. In the chaotic regime the fidelity decays at the same rate as the Lyapunov exponent, independent of noise magnitude, giving an efficient few-qubit signature of quantum chaos. We use the IBM-Q platform to test the ability of present day quantum hardware to realize these chaotic dynamics. First, we can observe the transition from diffusion to localization when using three qubits, but not more. Next, we demonstrate that with three qubits the fidelity decay distinguishes the dynamics, becoming more rapid as the dynamics become more chaotic in a manner that is independent of gate count. Finally, we show that measuring the Lyapunov exponent as a noise-independent fidelity decay requires at least six qubits with at least an order of magnitude less noise. *Prepared by LLNL under US DOE Contract DE-AC52-07NA27344.

(Session 5 : Thursday from 12:00pm-2:00 pm)