Minimum-Time Selective Control of Homonuclear Spins
arXiv:1607.03213 · doi:10.1109/TCST.2015.2390191
Abstract
In NMR (Nuclear Magnetic Resonance) quantum computation, the selective control of multiple homonuclear spins is usually slow because their resonance frequencies are very close to each other. To quickly implement controls against decoherence effects, this paper presents an efficient numerical algorithm fordesigning minimum-time local transformations in two homonuclear spins. We obtain an accurate minimum-time estimation via geometric analysis on the two-timescale decomposition of the dynamics. Such estimation narrows down the range of search for the minimum-time control with a gradient-type optimization algorithm. Numerical simulations show that this method can remarkably reduce the search efforts, especially when the frequency difference is very small and the control field is high. Its effectiveness is further demonstrated by NMR experiments with two homunuclear carbon spins in a trichloroethylene (C2H1Cl3) sample system.
8 pages, 6 figures
References in corpus (26)
- NMR Techniques for Quantum Control and Computation
- Time Optimal Control in Spin Systems
- Experimental Realization of Nonadiabatic Holonomic Quantum Computation
- Quantum Brachistochrone
- Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
- Modeling and Control of Quantum Systems: An Introduction
- Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
- Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic Field
- Benchmarking quantum control methods on a 12-qubit system
- Quantum Process Tomography of the Quantum Fourier Transform
- Liquid State NMR as a Test-bed for Developing Quantum Control Methods
- Time Optimal Unitary Operations
- An alternative quantum fidelity for mixed states of qudits
- Exploring the trade-off between fidelity- and time-optimal control of quantum unitary transformations
- Simultaneous time-optimal control of the inversion of two spin 1/2 particles
- Experimental implementation of encoded logical qubit operations in a perfect quantum error correcting code
- Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance
- Characterization of the Critical Submanifolds in Quantum Ensemble Control Landscapes
- Time-optimal synthesis of SU(2) transformations for a spin-1/2 system
- Quantum Brachistochrone for Mixed States
- Implementing quantum logic gates with GRAPE: principles and practicalities
- Implementation of Quantum Gates via Optimal Control
- Time-Optimal Transfer of Coherence
- Efficient synthesis of quantum gates on indirectly coupled spins
- Characterization of majorization monotone quantum dynamics
- Optimal coherent control of CARS: signal enhancement and background elimination
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