Inherently trap-free convex landscapes for full quantum optimal control

TL;DR

This paper proves that full quantum-quantum control landscapes are convex and free of traps, enabling efficient optimization of quantum systems controlled by quantum controllers, demonstrated with the Jaynes-Cummings model.

Contribution

It establishes the convexity and trap-free nature of full quantum-quantum control landscapes, a significant theoretical advancement in quantum control.

Findings

Landscapes are convex and trap-free.

All level sets are connected convex sets.

Optimal solutions can be efficiently computed numerically.

Abstract

We present a comprehensive analysis of the landscape for full quantum-quantum control associated with the expectation value of an arbitrary observable of one quantum system controlled by another quantum system. It is shown that such full quantum-quantum control landscapes are convex, and hence devoid of local suboptima and saddle points that may exist in landscapes for quantum systems controlled by time-dependent classical fields. There is no controllability requirement for the full quantum-quantum landscape to be trap-free, although the forms of Hamiltonians, the flexibility in choosing initial state of the controller, as well as the control duration, can infulence the reachable optimal value on the landscape. All level sets of the full quantum-quantum landscape are connected convex sets. Finally, we show that the optimal solution of the full quantum-quantum control landscape can be readily determined numerically, which is demonstrated using the Jaynes-Cummings model depicting a two-level atom interacting with a quantized radiation field.