Optimal control theory for a unitary operation under dissipative evolution

Abstract

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 $\sqrt{i{\rm{S}}WAP}$ gate with superconducting qubits.

Keywords

• quantum dissipative systems
• entanglement creation
• optimal control theory
• 02.30.Yy
• 03.65Yz
• 03.67.Bg