Experiments in coherent 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 to optimize the sensitivity of the experiments. Here, we present a novel approach for efficient control of dynamics in spin chains of arbitrary length. The approach relies on creating certain three spin encoded states, which can be efficiently transferred through a spin chain. The methods presented are expected to find applications in control of spin dynamics in coherent spectroscopy and quantum information processing.Experiments in coherent 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 to optimize the sensitivity of the experiments. Here, we present a novel approach for efficient control of dynamics in spin chains of arbitrary length. The approach relies on creating certain three spin encoded states, which can be efficiently transferred through a spin chain. The methods presented are expected to find applications in control of spin dynamics in coherent spectroscopy and quantum information processing.

Physical Review ADec 12, 200256 citations

Geodesics for efficient creation and propagation of order along Ising spin chains

Haidong Yuan, Steffen J. Glaser, Navin Khaneja

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 ${(2J)}^{\ensuremath{-}1}$ 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.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 ${(2J)}^{\ensuremath{-}1}$ 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.

arXiv:0705.0378Physical Review AJul 17, 200726 citations

Relaxation Optimized Polarization-Coherence Transfer in Ising Spin Chains

Dionisis Stefanatos, Navin Khaneja, Steffen J. Glaser

Experiments in coherent spectroscopy correspond to control of quantum-mechanical ensembles guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transfers should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in Nuclear Magnetic Resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of polarization or coherence transfer between coupled spins in the presence of relaxation. Furthermore, what is the optimal pulse sequence which achieves this efficiency? This letter is a continuation of our previous work on the above problems. Here, we attempt to answer these questions for an Ising spin chain, under the presence of transverse relaxation. The methods presented in this paper are expected to find applications not only in coherent spectroscopy but also in quantum information processing.Experiments in coherent spectroscopy correspond to control of quantum-mechanical ensembles guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transfers should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in Nuclear Magnetic Resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of polarization or coherence transfer between coupled spins in the presence of relaxation. Furthermore, what is the optimal pulse sequence which achieves this efficiency? This letter is a continuation of our previous work on the above problems. Here, we attempt to answer these questions for an Ising spin chain, under the presence of transverse relaxation. The methods presented in this paper are expected to find applications not only in coherent spectroscopy but also in quantum information processing.

May 15, 20050 citations

Optimal control of coupled spins in presence of longitudinal and transverse relaxation

Dionisis Stefanatos, Navin Khaneja, Steffen J. Glaser

Experiments in coherent spectroscopy correspond to control of quantum mechanical ensemble guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transformations should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in nuclear magnetic resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of coherence or polarization transfer between two spins in the presence of relaxation. Furthermore what is the optimal pulse sequence which achieves this efficiency? This manuscript extends our previous work in the above problems. Here, we take into account both the longitudinal and the transverse relaxation mechanisms, thus generalizing our previous results, where the former had been neglected.Experiments in coherent spectroscopy correspond to control of quantum mechanical ensemble guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transformations should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in nuclear magnetic resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of coherence or polarization transfer between two spins in the presence of relaxation. Furthermore what is the optimal pulse sequence which achieves this efficiency? This manuscript extends our previous work in the above problems. Here, we take into account both the longitudinal and the transverse relaxation mechanisms, thus generalizing our previous results, where the former had been neglected.

IEEE International Workshop on Workload Characterization (WWC)Apr 23, 20046 citations

Efficient synthesis of quantum gates on indirectly coupled spins

Haidong Yuan, Daxiu Wei, Yajuan Zhang +2 more

Experiments in coherent nuclear and electron magnetic resonance and quantum computing in general correspond to control of quantum-mechanical systems, 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 derive a time-optimal sequences as fundamental building blocks to synthesize unitary transformations. Such sequences can be widely implemented on various physical systems, including the simulation of effective Hamiltonians for topological quantum computing on spin lattices. Experimental demonstrations are provided for a system consisting of three nuclear spins.Experiments in coherent nuclear and electron magnetic resonance and quantum computing in general correspond to control of quantum-mechanical systems, 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 derive a time-optimal sequences as fundamental building blocks to synthesize unitary transformations. Such sequences can be widely implemented on various physical systems, including the simulation of effective Hamiltonians for topological quantum computing on spin lattices. Experimental demonstrations are provided for a system consisting of three nuclear spins.

arXiv:1309.3837Physical Review AApr 17, 201414 citations

Time optimal control in spin systems

Navin Khaneja, Roger W. Brockett, Steffen J. Glaser

In this paper, we study the design of pulse sequences for nuclear magnetic resonance spectroscopy as a problem of time optimal control of the unitary propagator. Radio-frequency pulses are used in coherent spectroscopy to implement a unitary transfer between states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group. What is the minimum time required to steer the system from some initial point to a specified final point? In nuclear magnetic resonance (NMR) spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two-spin system.In this paper, we study the design of pulse sequences for nuclear magnetic resonance spectroscopy as a problem of time optimal control of the unitary propagator. Radio-frequency pulses are used in coherent spectroscopy to implement a unitary transfer between states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group. What is the minimum time required to steer the system from some initial point to a specified final point? In nuclear magnetic resonance (NMR) spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two-spin system.

arXiv:quant-ph/0006114Physical Review AFeb 14, 2001741 citations

J

(in units of Hz), significantly faster than ${(2J)}^{\ensuremath{-}1}$ 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.