Optimal preparation of the W state for qubits with XY coupling

¹ Department of Physics and Astronomy, University of California - Los Angeles, CA 90095, USA
² Department of Physics and Astronomy, Western Washington University - Bellingham, WA 98225, USA
³ Advanced Materials Science and Engineering Center, Western Washington University - Bellingham, WA 98225, USA
⁴ Kavli Institute for Theoretical Physics, University of California - Santa Barbara, CA 93106, USA

Received: 1 May 2025
Accepted: 7 April 2026

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.