Algebraic synthesis of time-optimal unitaries in SU (2) with alternating controls

作者：Aiello Clarice D^*; Allegra Michele; Hemmerling Boerge; Wan Xiaoting; Cappellaro Paola

来源：Quantum Information Processing, 2015, 14(9): 3233-3256.

DOI：10.1007/s11128-015-1045-6

• Time-optimal control
• Quantum control
• Quantum information processing

We present an algebraic framework to study the time-optimal synthesis of arbitrary unitaries in SU (2), when the control set is restricted to rotations around two non-parallel axes in the Bloch sphere. Our method bypasses commonly used control-theoretical techniques and easily imposes necessary conditions on time-optimal sequences. In a straightforward fashion, we prove that time-optimal sequences are solely parametrized by three rotation angles and derive general bounds on those angles as a function of the relative rotation speed of each control and the angle between the axes. Results are substantially different whether both clockwise and counterclock-wise rotations about the given axes are allowed, or only clockwise rotations. In the first case, we prove that any finite time-optimal sequence is composed at most of five control concatenations, while for the more restrictive case, we present scaling laws on the maximum length of any finite time-optimal sequence. The bounds we find for both cases are stricter than previously published ones and severely constrain the structure of time-optimal sequences, allowing for an efficient numerical search of the time-optimal solution. Our results can be used to find the time-optimal evolution of qubit systems under the action of the considered control set and thus potentially increase the number of realizable unitaries before decoherence.

• 出版日期2015-9