Overcoming the su(2^n) sufficient condition for the coherent control of n-qubit systems

Details Overcoming the su(2^n) sufficient condition for the coherent control of n-qubit systems Overcoming the su(2^n) sufficient condition for the coherent control of n-qubit systems

2007-03-23

arxiv.org/abs/quant-ph/0703220v1

Physics

Quantum Physics

13 pp., 2 figures

Scientific paper

10.1103/PhysRevA.76.033401

We study quantum systems with even numbers N of levels that are completely state-controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than the respective su(N) with dimension N^2-1. We show that this reduction constrains the Hamiltonian to have symmetric energy levels. An example of such a system is an n-qubit system. Using a geometric representation for the quantum wave function of a finite system, we present an explicit example that shows a two-qubit system can be controlled by the elements of the Lie algebra sp(4) (isomorphic to spin(5) and so(5)) with dimension ten rather than su(4) with dimension fifteen. These results enable one to envision more efficient algorithms for the design of fields for quantum-state engineering, and they provide more insight into the fundamental structure of quantum control.

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