Broken symmetry in a two-qubit quantum control landscape

TL;DR

This paper investigates a phase transition in the optimal control protocols for a two-qubit system, revealing a symmetry-breaking phenomenon and its impact on entanglement and fidelity.

Contribution

It uncovers a discontinuous phase transition and symmetry-breaking in quantum control landscapes, with a developed mean-field theory explaining these phenomena.

Findings

Discontinuous phase transition below the quantum speed limit.

Symmetry-breaking in optimal control protocols.

Different entanglement entropies in degenerate high-fidelity states.

Abstract

We analyze the physics of optimal protocols to prepare a target state with high fidelity in a symmetrically coupled two-qubit system. By varying the protocol duration, we find a discontinuous phase transition, which is characterized by a spontaneous breaking of a $\mathbb{Z}_2$ symmetry in the functional form of the optimal protocol, and occurs below the quantum speed limit. We study in detail this phase and demonstrate that even though high-fidelity protocols come degenerate with respect to their fidelity, they lead to final states of different entanglement entropy shared between the qubits. Consequently, while globally both optimal protocols are equally far away from the target state, one is locally closer than the other. An approximate variational mean-field theory which captures the physics of the different phases is developed.