2016/07/10 by Navin Khaneja, Khaneja, Navin
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · #Advanced NMR Techniques and Applications #Electron Spin Resonance Studies #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1607.02692
openalex publication_date 2016/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study some control problems that derive from time optimal control of coupled spin dynamics in NMR spectroscopy and quantum information and computation. Time optimal control helps to minimize relaxation losses. The ability to synthesize, local unitaries, much more rapidly than evolution of couplings, gives a natural time scale separation in these problems. The generators of evolution, \g, are decomposed into fast generators \k (local Hamiltonians) and slow generators \p (couplings) as a Cartan decomposition \g = \p ⊕ \k. Using this decomposition, we exploit some convexity ideas to completely characterize the reachable set and time optimal control for these problems. In this paper, we carry out a second order analysis of time optimality.