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Quantum control landscape of bipartite systems

Journal Article · · Journal of Physics. A, Mathematical and Theoretical
 [1];  [2];  [2]
  1. SC Solutions, Sunnyvale, CA (United States); DOE/OSTI
  2. Princeton Univ., NJ (United States)
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The control landscape of a quantum system A interacting with another quantum system B is studied. Only system A is accessible through time dependent controls, while system B is not accessible. The objective is to find controls that implement a desired unitary transformation on A, regardless of the evolution on B, at a sufficiently large final time. The freedom in the evolution on B is used to define an extended control landscape on which the critical points are investigated in terms of kinematic and dynamic gradients. A spectral decomposition of the corresponding extended unitary system simplifies the landscape analysis which provides: (i) a sufficient condition on the rank of the dynamic gradient of the extended landscape that guarantees a trap free search for the final time unitary matrix of system A, and (ii) a detailed decomposition of the components of the overall dynamic gradient matrix. Consequently, if the rank condition is satisfied, a gradient algorithm will find the controls that implements the target unitary on system A. It is shown that even if the dynamic gradient with respect to the controls alone is not full rank, the additional flexibility due to the parameters that define the extended landscape still can allow for the rank condition of the extended landscape to hold. Moreover, satisfaction of the latter rank condition subsumes any assumptions about controllability, reachability and control resources. Here satisfaction of the rank condition is taken as an assumption. The conditions which ensure that it holds remain an open research question. We lend some numerical support with two common examples for which the rank condition holds.

Research Organization:
Princeton Univ., NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
FG02-02ER15344
OSTI ID:
1609375
Alternate ID(s):
OSTI ID: 22985421
Journal Information:
Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 16 Vol. 52; ISSN 1751-8113
Publisher:
IOP PublishingCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

97 MATHEMATICS AND COMPUTING