Time-optimal monotonic convergent algorithms for the control of quantum systems

TL;DR

This paper introduces a novel monotonic convergence algorithm that optimizes both control duration and field fluence for quantum system control, demonstrated on NMR spin systems for implementing quantum gates.

Contribution

It extends existing algorithms by including control duration optimization in the cost functional for quantum control tasks.

Findings

Successfully optimized control duration and fluence in quantum systems.

Implemented CNOT gates in two- and four-spin NMR systems.

Demonstrated improved control strategies over traditional fixed-duration methods.

Abstract

We present a new formulation of monotonically convergent algorithms which allows to optimize both the control duration and the field fluence. A standard algorithm designs a control field of fixed duration which both brings the system close to the target state and minimizes its fluence, whereas here we include in addition the optimization of the duration in the cost functional. We apply this new algorithm to the control of spin systems in Nuclear Magnetic Resonance. We show how to implement CNOT gates in systems of two and four coupled spins.