Topological Phase Transitions in a Constrained Two-Qubit Quantum Control Landscape

TL;DR

This paper uncovers a new class of control landscape phase transitions in quantum control, linked to topological changes in optimal protocol sets, with implications for experimental detection.

Contribution

It introduces topological phase transitions in quantum control landscapes, revealing how the structure of optimal protocols changes with protocol duration in a two-qubit system.

Findings

Discontinuous changes in the number of connected components of optimal protocols.

Topological CLPTs can be detected experimentally.

Control landscape topology influences quantum control efficiency.

Abstract

In optimal quantum control, control landscape phase transitions (CLPTs) indicate sharp changes occurring in the set of optimal protocols, as a physical model parameter is varied. Here, we demonstrate the existence of a new class of CLPTs, associated with changes in the topological properties of the optimal level set in a two-qubit state-preparation problem. In particular, the distance distribution of control protocols sampled through stochastic homotopic dynamics reveals discontinuous changes in the number of connected components in the optimal level set, as a function of the protocol duration. We demonstrate how topological CLPTs can be detected in modern-day experiments.