Time optimal control of coupled spin dynamics: A global analysis

Dominique Sugny

Navin Khaneja

In this chapter, 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.In a two qubit system, 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 unitary evolution, g, are decomposed into fast generators k (local Hamiltonians) and slow generators p (couplings) as a Cartan decomposition g ¼ p ⊕ k.Using this decomposition, we exploit some convexity ideas to completely characterize the reachable set and time optimal control for these problems.The main contribution of the chapter is, we carry out a global analysis of time optimality.

Steffen J. Glaser

Navin Khaneja

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 $\g = \p \oplus \k$. 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.

Yasuhiro Aota, Yuichiro Mori, Takahiko Satoh +2 more

Interacting spin ensembles are promising platforms for quantum sensing, but spin-spin interactions can induce complex, nonmonotonic responses to external fields, limiting the dynamic range over which the fields can be estimated unambiguously. Here, we propose a quantum-circuit-learning-inspired method to improve the dynamic range of interacting quantum sensors using optimized global control fields. We consider an ensemble of dipole-coupled spins subjected to an inhomogeneous magnetic field generated by an electric current. By optimizing the global control fields applied during sensing, we train the expectation value of the collective magnetization to approximate a prescribed monotonic target function. We also introduce a penalty on the magnetization variance to account for measurement fluctuations. Numerical simulations demonstrate that the optimized control can substantially enlarge the dynamic range compared with sensing without control. We further investigate the trade-off between dynamic range and estimation uncertainty and show that the variance penalty can reduce the uncertainty at the expense of dynamic range. These results demonstrate that learning-assisted global control provides a promising approach to improving the performance of interacting quantum sensors.

Seth Merkel, Souma Chaudhury, Andrew Silberfarb +3 more