Dissipative Quantum Dynamics and Optimal Control using Iterative Time Ordering: An Application to Superconducting Qubits

TL;DR

This paper introduces an iterative time-ordering quantum propagator combined with optimal control theory, applied to superconducting qubits, highlighting its efficiency and limitations in handling strong time-dependent dynamics.

Contribution

It develops and tests a quantum propagator that explicitly accounts for time ordering, enhancing control over superconducting qubits with complex time-dependent behavior.

Findings

The propagator efficiently models superconducting circuit dynamics.

Performance sensitivity to time-dependence strength affects optimal control.

Quantum gate fidelity and speed are analyzed within this framework.

Abstract

We combine a quantum dynamical propagator that explicitly accounts for quantum mechanical time ordering with optimal control theory. After analyzing its performance with a simple model, we apply it to a superconducting circuit under so-called Pythagorean control. Breakdown of the rotating-wave approximation is the main source of the very strong time-dependence in this example. While the propagator that accounts for the time ordering in an iterative fashion proves its numerical efficiency for the dynamics of the superconducting circuit, its performance when combined with optimal control turns out to be rather sensitive to the strength of the time-dependence. We discuss the kind of quantum gate operations that the superconducting circuit can implement including their performance bounds in terms of fidelity and speed.