TY - JOUR

T1 - Near-time-optimal control for quantum systems

AU - Chen, Qi Ming

AU - Wu, Re Bing

AU - Zhang, Tian Ming

AU - Rabitz, Herschel

N1 - Publisher Copyright:
© 2015 American Physical Society.

PY - 2015/12/16

Y1 - 2015/12/16

N2 - For a quantum system controlled by an external field, time-optimal control is referred to as the shortest-time-duration control that can still permit maximizing an objective function J, which is especially a desirable goal for engineering quantum dynamics against decoherence effects. However, since rigorously finding a time-optimal control is usually very difficult and in many circumstances the control is only required to be sufficiently short and precise, one can design algorithms seeking such suboptimal control solutions for much reduced computational effort. In this paper, we propose an iterative algorithm for finding near-time-optimal control in a high level set (i.e., the set of controls that achieves the same value of J) that can be arbitrarily close to the global optima. The algorithm proceeds seeking to decrease the time duration T while the value of J remains invariant, until J leaves the level-set value; the deviation of J due to numerical errors is corrected by gradient climbing that brings the search back to the level-set J value. Since the level set is very close to the maximum value of J, the resulting control solution is nearly time optimal with manageable precision. Numerical examples demonstrate the effectiveness and general applicability of the algorithm.

AB - For a quantum system controlled by an external field, time-optimal control is referred to as the shortest-time-duration control that can still permit maximizing an objective function J, which is especially a desirable goal for engineering quantum dynamics against decoherence effects. However, since rigorously finding a time-optimal control is usually very difficult and in many circumstances the control is only required to be sufficiently short and precise, one can design algorithms seeking such suboptimal control solutions for much reduced computational effort. In this paper, we propose an iterative algorithm for finding near-time-optimal control in a high level set (i.e., the set of controls that achieves the same value of J) that can be arbitrarily close to the global optima. The algorithm proceeds seeking to decrease the time duration T while the value of J remains invariant, until J leaves the level-set value; the deviation of J due to numerical errors is corrected by gradient climbing that brings the search back to the level-set J value. Since the level set is very close to the maximum value of J, the resulting control solution is nearly time optimal with manageable precision. Numerical examples demonstrate the effectiveness and general applicability of the algorithm.

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U2 - 10.1103/PhysRevA.92.063415

DO - 10.1103/PhysRevA.92.063415

M3 - Article

AN - SCOPUS:84950138308

SN - 1050-2947

VL - 92

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 6

M1 - 063415

ER -