Optimal preparation of the $W$ state for qubits with XY coupling

TL;DR

This paper uses optimal control theory and simulated annealing to design efficient protocols for preparing three-qubit W states with XY coupling, considering practical constraints and robustness.

Contribution

It introduces a method combining simulated annealing and Pontryagin's principle to find and characterize optimal pulse protocols for W state preparation.

Findings

Optimal protocols achieve high fidelity within quantum speed limits.

Protocols are robust to implementation errors and decoherence.

Pontryagin's principle effectively guides pulse shape design.

Abstract

Using simulated annealing, we find optimal protocols that evolve a simple product state into a three-qubit $W$ state with a Hamiltonian that describes XY coupling and single-qubit gates, and determine the associated quantum speed limit. Applying Pontryagin's minimum principle, we fully characterize the optimal bang-bang protocols. While leakage affects performance, the protocols remain robust to implementation errors and operate well within relaxation and decoherence times. Our findings highlight Pontryagin's principle as a powerful tool for designing pulse shapes that directly link device interactions to specific quantum gates and target states.