Geometric quantum computation using fictitious spin-(1/2) subspaces of strongly dipolar coupled nuclear spins

Gopinath, T; Kumar, Anil

doi:10.1103/PHYSREVA.73.022326

Title: Geometric quantum computation using fictitious spin-(1/2) subspaces of strongly dipolar coupled nuclear spins

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Abstract

Geometric phases have been used in NMR to implement controlled phase shift gates for quantum-information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems by using nonadiabatic geometric phases, obtained by evolving the magnetization of fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces is refocused by a spin echo pulse sequence and by setting the delay of transition selective pulses such that the evolution under the homonuclear coupling makes a complete 2{pi} rotation. A detailed theoretical explanation of nonadiabatic geometric phases in NMR is given by using single transition operators. Controlled phase shift gates, two qubit Deutsch-Jozsa algorithm, and parity algorithm in a qubit-qutrit system have been implemented in various strongly dipolar coupled systems obtained by orienting the molecules in liquid crystal media.

Authors:

Gopinath, T; Kumar, Anil ^[1]

NMR Quantum Computing and Quantum Information Group, Department of Physics, and NMR Research Centre, Indian Institute of Science, Bangalore-560012 (India)

Publication Date:: Wed Feb 15 00:00:00 EST 2006

OSTI Identifier:: 20974542

Resource Type:: Journal Article

Journal Name:: Physical Review. A

Additional Journal Information:: Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.022326; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; LIQUID CRYSTALS; MAGNETIZATION; NUCLEAR MAGNETIC RESONANCE; PHASE SHIFT; PULSES; QUANTUM COMPUTERS; QUANTUM INFORMATION; QUANTUM MECHANICS; QUBITS; SPIN; WEAK-COUPLING MODEL

Citation Formats


                    Gopinath, T, and Kumar, Anil. Geometric quantum computation using fictitious spin-(1/2) subspaces of strongly dipolar coupled nuclear spins.  United States: N. p., 2006. 
        Web.  doi:10.1103/PHYSREVA.73.022326.

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                    Gopinath, T, & Kumar, Anil. Geometric quantum computation using fictitious spin-(1/2) subspaces of strongly dipolar coupled nuclear spins.  United States.  https://doi.org/10.1103/PHYSREVA.73.022326

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                    Gopinath, T, and Kumar, Anil. 2006.  
        "Geometric quantum computation using fictitious spin-(1/2) subspaces of strongly dipolar coupled nuclear spins".  United States.  https://doi.org/10.1103/PHYSREVA.73.022326.

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@article{osti_20974542,

  title        = {Geometric quantum computation using fictitious spin-(1/2) subspaces of strongly dipolar coupled nuclear spins},

  author       = {Gopinath, T and Kumar, Anil},

  abstractNote = {Geometric phases have been used in NMR to implement controlled phase shift gates for quantum-information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems by using nonadiabatic geometric phases, obtained by evolving the magnetization of fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces is refocused by a spin echo pulse sequence and by setting the delay of transition selective pulses such that the evolution under the homonuclear coupling makes a complete 2{pi} rotation. A detailed theoretical explanation of nonadiabatic geometric phases in NMR is given by using single transition operators. Controlled phase shift gates, two qubit Deutsch-Jozsa algorithm, and parity algorithm in a qubit-qutrit system have been implemented in various strongly dipolar coupled systems obtained by orienting the molecules in liquid crystal media.},

  doi          = {10.1103/PHYSREVA.73.022326},

  url          = {https://www.osti.gov/biblio/20974542},
  journal      = {Physical Review. A},

  issn         = {1050-2947},

  number       = 2,

  volume       = 73,

  place        = {United States},

  year         = {Wed Feb 15 00:00:00 EST 2006},

  month        = {Wed Feb 15 00:00:00 EST 2006}

}

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