Broadband Geodesic Pulses for Three Spin Systems: Time-Optimal Realization of Effective Trilinear Coupling Terms and Indirect SWAP Gates

Broadband implementations of time-optimal geodesic pulse elements are introduced for the efficient creation of effective trilinear coupling terms for spin systems consisting of three weakly coupled spins 1/2. Based on these pulse elements, the time-optimal implementation of indirect SWAP operations is demonstrated experimentally. The duration of indirect SWAP gates based on broadband geodesic sequence is reduced by 42.3% compared to conventional approaches.Comment: 22 pages, incl. 8 figure

Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance

The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.Comment: 30 pages, 13 figur

Feasibility Study of a Satellite Solar Power Station

A feasibility study of a satellite solar power station (SSPS) was conducted to: (1) explore how an SSPS could be flown and controlled in orbit; (2) determine the techniques needed to avoid radio frequency interference (RFI); and (3) determine the key environmental, technological, and economic issues involved. Structural and dynamic analyses of the SSPS structure were performed, and deflections and internal member loads were determined. Desirable material characteristics were assessed and technology developments identified. Flight control performance of the SSPS baseline design was evaluated and parametric sizing studies were performed. The study of RFI avoidance techniques covered (1) optimization of the microwave transmission system; (2) device design and expected RFI; and (3) SSPS RFI effects. The identification of key issues involved (1) microwave generation, transmissions, and rectification and solar energy conversion; (2) environmental-ecological impact and biological effects; and (3) economic issues, i.e., costs and benefits associated with the SSPS. The feasibility of the SSPS based on the parameters of the study was established

Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer

Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be saved in producing an effective Hamiltonian, if spin-decoupling is avoided. We provide time optimal pulse sequences for producing an important class of effective Hamiltonians in three spin networks. These effective Hamiltonians are useful for coherence transfer experiments and implementation of quantum logic gates in NMR quantum computing. It is demonstrated that computing these time optimal pulse sequences can be reduced to geometric problems that involve computing sub-Riemannian geodesics on Homogeneous spaces

Geodesics for Efficient Creation and Propagation of Order along Ising Spin Chains

Experiments in coherent nuclear and electron magnetic resonance, and optical spectroscopy correspond to control of quantum mechanical ensembles, guiding them from initial to final target states by unitary transformations. The control inputs (pulse sequences) that accomplish these unitary transformations should take as little time as possible so as to minimize the effects of relaxation and decoherence and to optimize the sensitivity of the experiments. Here we give efficient syntheses of various unitary transformations on Ising spin chains of arbitrary length. The efficient realization of the unitary transformations presented here is obtained by computing geodesics on a sphere under a special metric. We show that contrary to the conventional belief, it is possible to propagate a spin order along an Ising spin chain with coupling strength J (in units of Hz), significantly faster than 1/(2J) per step. The methods presented here are expected to be useful for immediate and future applications involving control of spin dynamics in coherent spectroscopy and quantum information processing

Optimal control of circuit quantum electrodynamics in one and two dimensions

Optimal control can be used to significantly improve multi-qubit gates in quantum information processing hardware architectures based on superconducting circuit quantum electrodynamics. We apply this approach not only to dispersive gates of two qubits inside a cavity, but, more generally, to architectures based on two-dimensional arrays of cavities and qubits. For high-fidelity gate operations, simultaneous evolutions of controls and couplings in the two coupling dimensions of cavity grids are shown to be significantly faster than conventional sequential implementations. Even under experimentally realistic conditions speedups by a factor of three can be gained. The methods immediately scale to large grids and indirect gates between arbitrary pairs of qubits on the grid. They are anticipated to be paradigmatic for 2D arrays and lattices of controllable qubits.Comment: Published version