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

Quantum computers promise to deliver large gains in computational power that can potentially be used to benefit the Fusion Energy Sciences (FES) program. Through the quantum-classical correspondence principle, future error-corrected quantum computers should eventually be able to simulate classical dynamical systems. The quantum dynamics also efficiently encodes classical dynamical information in the decay of the fidelity. However, if the effective Planck’s constant is too large, the quantum system will display dynamical Anderson localization rather than classically chaotic diffusion.

Here we study the simplest types of quantum chaotic dynamical systems, quantum maps, namely the quantum sawtooth map [G. Benenti, et al. Phys. Rev. Lett. 87, 227901-1 (2001)]. We simulate this map using the IBM-Q quantum hardware platform. We then demonstrate that with three qubits dynamical localization leads to a slowed fidelity decay. We finally show that, in principle, the Lyapunov exponent can be measured as a noise-independent fidelity decay on systems with as few as six qubits.