2009/04/29 by Uwe Sander, Sander, U., T. Schulte-Herbrueggen +1
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #FOS: Physical sciences #Molecular spectroscopy and chirality #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.0904.4654
openalex publication_date 2009/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric) experimental coupling architecture several decision problems can be solved in a unified way: (i) can a target Hamiltonian be simulated? (ii) can a target gate be synthesised? (iii) to which extent is the system observable by a given set of detection operators? and, as a special case of the latter, (iv) can an underlying system Hamiltonian be identified with a given set of detection operators? Finally, in turn, lack of symmetry provides a convenient necessary condition for full controllability. Though often easier to assess than the well-established Lie-algebra rank condition, this is not sufficient unless the candidate dynamic simple Lie algebra can be pre-identified uniquely, which is fortunately less complicated than expected.