Optimal control theory for a unitary operation under dissipative evolution

摘要

We show that optimizing a quantum gate for an open quantum system requiresthe time evolution of only three states irrespective of the dimension ofHilbert space. This represents a significant reduction in computationalresources compared to the complete basis of Liouville space that is commonlybelieved 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 timeevolution of two properly chosen states is sufficient to distinguish any twounitaries. We illustrate gate optimization employing a reduced set of statesfor a controlled phasegate with trapped atoms as qubit carriers and a$\sqrt{i\text{SWAP}}$ gate with superconducting qubits.