We derive the explicit solution of the problem of time-optimal control by a common magnetic field for two independent spin- $\frac{1}{2}$ particles. Our approach is based on the Pontryagin maximum principle and a symmetry reduction technique. We experimentally implement the optimal control using zero-field nuclear magnetic resonance. This reveals an average gate error of $1%$ and a 70-- $80%$ decrease in the experiment duration as compared to existing methods. This analytical solution and experimental demonstration of time-optimal control in such a system provides a route to achieve time-optimal control in more general quantum systems.We derive the explicit solution of the problem of time-optimal control by a common magnetic field for two independent spin-$\frac{1}{2}$ particles. Our approach is based on the Pontryagin maximum principle and a symmetry reduction technique. We experimentally implement the optimal control using zero-field nuclear magnetic resonance. This reveals an average gate error of $1%$ and a 70--$80%$ decrease in the experiment duration as compared to existing methods. This analytical solution and experimental demonstration of time-optimal control in such a system provides a route to achieve time-optimal control in more general quantum systems.

arXiv:1810.07905Physical Review ADec 7, 201810 citations

TIME-OPTIMAL CONTROL OF A DISSIPATIVE SPIN 1/2 PARTICLE

Dominique Sugny, M. Lapert, Elie Assémat

World scientific series on nonlinear science, series BJun 1, 20100 citations

Time optimal control in coupled spin systems: a second order analysis

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.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.

arXiv:1607.02692Jul 10, 20162 citations

Exact solutions for time-optimal control of spin

I=1

I = 1 by NMR

We derive the explicit solution of the problem of time-optimal control by a common magnetic field for two independent spin-

\frac{1}{2}

particles. Our approach is based on the Pontryagin maximum principle and a symmetry reduction technique. We experimentally implement the optimal control using zero-field nuclear magnetic resonance. This reveals an average gate error of

1%

and a 70--

80%

decrease in the experiment duration as compared to existing methods. This analytical solution and experimental demonstration of time-optimal control in such a system provides a route to achieve time-optimal control in more general quantum systems.