CONTROL OF QUANTUM SYSTEMS

• Published in: International journal of modern physics. B, Condensed matter physics, statistical physics, applied physics Vol. 17; no. 28; pp. 5397 - 5411
• Main Authors: CLARK, JOHN W., LUCARELLI, DENNIS G., TARN, TZYH-JONG
• Format: Journal Article
• Language: English
• Published: World Scientific Publishing Company 10.11.2003
• Subjects: New Frontier and Methods
• ISSN: 0217-9792; 1793-6578
• DOI: 10.1142/S021797920302051X

A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed against the background of recent ideas and advances in two seemingly disparate endeavours: (i) laser control of chemical reactions and (ii) quantum computation. Using Lie-algebraic methods, sufficient conditions have been derived for global controllability on a finite-dimensional manifold of an infinite-dimensional Hilbert space, in the case that the Hamiltonian and control operators, possibly unbounded, possess a common dense domain of analytic vectors. Some simple examples are presented. A synergism between quantum control and quantum computation is creating a host of exciting new opportunities for both activities. The impact of these developments on computational many-body theory could be profound.