Controllability of quantum mechanical systems by root space decomposition of su(N)

By Claudio Altafini. 2001

193 citations recorded by the source corpus.

The controllability property of the unitary propagator of an N-level quantum mechanical system subject to a single control field is described using the structure theory of semisimple Lie algebras. Sufficient conditions are provided for the vector fields in a generic configuration as well as in a few degenerate cases.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a378bed05fbb9ebe201cd52cd2cb8d86ade1c4da

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In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Quantum control of molecular rotation (2018, background): “The mathematical theory of controllability is by now well established for finite-dimensional closed quantum systems (Altafini, 2002; Albertini and D’Alessandro, 2003; Kurniawan, Dirr, and Helmke, 2012).”
Controllability of the discrete-spectrum Schrödinger equation driven by an external field (2008, background): “, for spin systems or for molecular dynamics when one neglects interactions with highly excited levels (see for instance [8, 19]).”
Quantum control theory and applications: A survey (2009, unknown): “Some algorithms have been developed for testing the controllability of speciﬁc quantum systems [20], [22], [25], [98].”
Local controllability of 1D linear and nonlinear Schr (2010, unknown): “The controllability of (17) is linked to the rank of the Lie algebra spanned by H0 and H1 (see for instance [5] by Albertini and D'Alessandro, [7] by Alta ni, [26] by Brockett, see also [3] by Agrachev and Sachkov, [32] by Coron for a more general discussion).”
Training Schrödinger’s cat: quantum optimal control (2015, background): “The difficulty of using the rank condition in large systems has motivated a geometric approach based on graph theory [8], yielding eventually a complete set of symmetry criteria for controllability [463].”
Controllability properties for finite dimensional quantum Markovian master equations (2002, background): “In fact, the corresponding basis in the adjoint representation is given by the n × n matrices adλ1 , . . . adλn of elements (adλl)jk = ifljk with fljk real fully skew-symmetric (with respect to the permutation of any pair of indexes) tensor.”