Title :
Symmetry principles in quantum system theory of multi-qubit systems made simple
Author :
Schulte-Herbrüggen, Thomas ; Sander, Uwe ; Zeier, Robert
Author_Institution :
Dept. of Chem., Tech. Univ. of Munich (TUM), Garching, Germany
Abstract :
Controllability and observability of multi-spin systems in architectures of various symmetries of coupling type and topology are investigated. We complement recent work of explicitly determining the respective dynamic system Lie algebras and thereby also precise reachability sets under symmetry constraints. Here the focus is on the converse: under which conditions can the absence of symmetry be taken as an indicator of universality of the hardware architecture? More precisely, the absence of symmetry implies irreducibility and provides a convenient necessary condition for full controllability. Though much easier to assess than the well-established Lie-algebra rank condition, this is not sufficient unless in an n-qubit system with connected coupling topology the candidate dynamic simple Lie algebra can be identified uniquely as the full unitary algebra su(2n). - Here we discuss simple tests confined to solving homogeneous linear equations in order to filter irreducible unitary representations of other candidate algebras of classical type (orthogonal ones and unitary symplectic ones). Finally, we give an outlook under which conditions algebras of exceptional type can also be ruled out.
Keywords :
Lie algebras; controllability; observability; quantum computing; reachability analysis; Lie-algebra rank condition; controllability; full unitary algebra su(2n); homogeneous linear equation; multiqubit system; multispin system; observability; quantum system theory; reachability sets; symmetry principle; Algebra; Computational modeling; Control systems; Controllability; Equations; Lattices; Process control; Quantum computing; Quantum mechanics; Topology;
Conference_Titel :
Communications, Control and Signal Processing (ISCCSP), 2010 4th International Symposium on
Conference_Location :
Limassol
Print_ISBN :
978-1-4244-6285-8
DOI :
10.1109/ISCCSP.2010.5463440