Optimal Control of Superconducting N-level quantum systems

TL;DR

This paper applies optimal control theory to a superconducting quantum system modeled as a multilevel quantum particle, demonstrating how to design control fields for state transfer with considerations of robustness.

Contribution

It formulates the control problem for a superconducting N-level system within optimal control theory and derives specific control fields using spectral filtering techniques.

Findings

Optimal control fields can coherently transfer populations between quantum states.

The control signals are carrier waves with time-varying amplitude and phase.

Sensitivity analysis shows robustness of the control solutions.

Abstract

We consider a current-biased dc SQUID in the presence of an applied time-dependent bias current or magnetic flux. The phase dynamics of such a Josephson device is equivalent to that of a quantum particle trapped in a $1-$D anharmonic potential, subject to external time-dependent control fields, {\it i.e.} a driven multilevel quantum system. The problem of finding the required time-dependent control field that will steer the system from a given initial state to a desired final state at a specified final time is formulated in the framework of optimal control theory. Using the spectral filter technique, we show that the selected optimal field which induces a coherent population transfer between quantum states is represented by a carrier signal having a constant frequency but which is time-varied both in amplitude and phase. The sensitivity of the optimal solution to parameter perturbations is also addressed.