We show that optimizing a quantum gate for an open quantum system requires the time evolution of only three states irrespective of the dimension of Hilbert space. This represents a significant reduction in computational resources compared to the complete basis of Liouville space that is commonly believed necessary for this task. The reduction is based on two observations: The target is not a general dynamical map but a unitary operation; and the time evolution of two properly chosen states is sufficient to distinguish any two unitaries. We illustrate gate optimization employing a reduced set of states for a controlled phasegate with trapped atoms as qubit carriers and a iSWAP gate with superconducting qubits.
@article{arxiv.1312.0111,
title = {Optimal control theory for a unitary operation under dissipative evolution},
author = {Michael H. Goerz and Daniel M. Reich and Christiane P. Koch},
journal= {arXiv preprint arXiv:1312.0111},
year = {2021}
}
Comments
22 pages, 10 figures. Correcting a typographical error in Eq. (9b) and adding Appendix B