Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0906.0474 · Physical Review A

Geometric quantum gates in liquid-state NMR based on a cancellation of dynamical phases

Yukihiro Ota, Yoshito Goto, Yasushi Kondo, Mikio Nakahara

Published Nov 10, 2009• 27 citations
arXivHTMLPDF

Abstract

A proposal for applying nonadiabatic geometric phases to quantum computing, called double-loop method [S.-L. Zhu and Z. D. Wang, Phys. Rev. A 67, 022319 (2003)], is demonstrated in a liquid-state nuclear magnetic-resonance quantum computer. Using a spin-echo technique, the original method is modified so that quantum gates are implemented in a standard high-precision nuclear magnetic-resonance system for chemical analysis. We show that a dynamical phase is successfully eliminated and a one-qubit quantum gate is realized although the gate fidelity is not high.

DOI
10.1103/physreva.80.052311

Related papers

Geometric quantum computation using fictitious spin- 12 subspaces of strongly dipolar coupled nuclear spins

Tata Gopinath, Anil Kumar

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 $2\ensuremath{\pi}$ 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.

arXiv:quant-ph/0607007•Physical Review A•Feb 16, 2006•20 citations

Nonadiabatic geometric quantum computation using a single-loop scenario

Xin-Ding Zhang, Shi-Liang Zhu, Lian Hu +1 more

A single-loop scenario is proposed to realize nonadiabatic geometric quantum computation. Conventionally, a so-called multiloop approach is used to remove the dynamical phase accumulated in the operation process for geometric quantum gates. More intriguingly, we here illustrate in detail how to use a special single-loop method to remove the dynamical phase and thus to construct a set of universal quantum gates based on the nonadiabatic geometric phase shift. The present scheme is applicable to NMR systems and may be feasible in other physical systems.

arXiv:quant-ph/0502090•Physical Review A•Jan 4, 2005•46 citations

Nonadiabatic geometric quantum computation

Zhisong Wang, Chunfeng Wu, Xun‐Li Feng +4 more

A different way to realize nonadiabatic geometric quantum computation is proposed by varying parameters in the Hamiltonian for nuclear-magnetic resonance, where the dynamical and geometric phases are implemented separately without the usual operational process. Therefore the phase accumulated in the geometric gate is a pure geometric phase for any input state. In comparison with the conventional geometric gates by rotating operations, our approach simplifies experimental implementations making them robust to certain experimental errors. In contrast to the unconventional geometric gates, our approach distinguishes the total and geometric phases and offers a wide choice of the relations between the dynamical and geometric phases.

Physical Review A•Oct 5, 2007•134 citations

Experimental implementation of high-fidelity unconventional geometric quantum gates using an NMR interferometer

Jiangfeng Du, Ping Zou, Z. D. Wang

Following a key idea of unconventional geometric quantum computation developed earlier [S. L. Zhu and Z. D. Wang, Phys. Rev. Lett. 91, 187902 (2003)], here we propose a more general scheme in such an intriguing way: ${\ensuremath{\gamma}}_{d}={\ensuremath{\alpha}}_{g}+\ensuremath{\eta}{\ensuremath{\gamma}}_{g}$, where ${\ensuremath{\gamma}}_{d}$ and ${\ensuremath{\gamma}}_{g}$ are respectively the dynamic and geometric phases accumulated in the quantum gate operation, with $\ensuremath{\eta}$ as a constant and ${\ensuremath{\alpha}}_{g}$ being dependent only on the geometric feature of the operation. More interestingly, we demonstrate an experiment to implement a universal set of such kind of generalized unconventional geometric quantum gates with high fidelity in an NMR system.

arXiv:quant-ph/0512036•Physical Review A•Aug 23, 2006•69 citations

Proper magnetic fields for nonadiabatic geometric quantum gates in NMR

Kazuto Oshima, Koji Azuma

In a scheme of nonadiabatic purely geometric quantum gates in nuclear-magnetic-resonance systems we propose proper magnitudes of magnetic fields that are suitable for an experiment. We impose a natural condition and reduce the degree of freedom of the magnetic fields to the extent. By varying the magnetic fields with essentially a one-dimensional degree of freedom, any spin state can acquire an arbitrary purely geometric phase ${\ensuremath{\varphi}}_{g}=\ensuremath{-}2\ensuremath{\pi}(1\ensuremath{-}\mathrm{cos}\ensuremath{\theta}),$ $0<~\mathrm{cos}\ensuremath{\theta}<~1.$ This is an essential ingredient for constructing universal geometric quantum gates.

arXiv:quant-ph/0305109•Physical Review A•Sep 10, 2003•6 citations

Operating a geometric quantum gate by external controllable parameters

Yinghua Ji, Shihua Cai, Le Jian-Xin +1 more

A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single-qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magnetic field parameters, one can let the dynamic phase be proportional to the geometric phase. Then, by controlling the azimuthal angle in the initial state, we may realize a geometric quantum gate whose fidelity is equal to one under cyclic evolution. This means that the quantum information is no distortion in the process of geometric quantum computation.

Chinese Physics B•Jan 1, 2010•2 citations
A proposal for applying nonadiabatic geometric phases to quantum computing, called double-loop method [S.-L. Zhu and Z. D. Wang, Phys. Rev. A 67, 022319 (2003)], is demonstrated in a liquid-state nuclear magnetic-resonance quantum computer. Using a spin-echo technique, the original method is modified so that quantum gates are implemented in a standard high-precision nuclear magnetic-resonance system for chemical analysis. We show that a dynamical phase is successfully eliminated and a one-qubit quantum gate is realized although the gate fidelity is not high.
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∕21∕21∕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 $2\ensuremath{\pi}$ 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.
A single-loop scenario is proposed to realize nonadiabatic geometric quantum computation. Conventionally, a so-called multiloop approach is used to remove the dynamical phase accumulated in the operation process for geometric quantum gates. More intriguingly, we here illustrate in detail how to use a special single-loop method to remove the dynamical phase and thus to construct a set of universal quantum gates based on the nonadiabatic geometric phase shift. The present scheme is applicable to NMR systems and may be feasible in other physical systems.
A different way to realize nonadiabatic geometric quantum computation is proposed by varying parameters in the Hamiltonian for nuclear-magnetic resonance, where the dynamical and geometric phases are implemented separately without the usual operational process. Therefore the phase accumulated in the geometric gate is a pure geometric phase for any input state. In comparison with the conventional geometric gates by rotating operations, our approach simplifies experimental implementations making them robust to certain experimental errors. In contrast to the unconventional geometric gates, our approach distinguishes the total and geometric phases and offers a wide choice of the relations between the dynamical and geometric phases.
Following a key idea of unconventional geometric quantum computation developed earlier [S. L. Zhu and Z. D. Wang, Phys. Rev. Lett. 91, 187902 (2003)], here we propose a more general scheme in such an intriguing way: ${\ensuremath{\gamma}}_{d}={\ensuremath{\alpha}}_{g}+\ensuremath{\eta}{\ensuremath{\gamma}}_{g}$, where ${\ensuremath{\gamma}}_{d}$ and ${\ensuremath{\gamma}}_{g}$ are respectively the dynamic and geometric phases accumulated in the quantum gate operation, with $\ensuremath{\eta}$ as a constant and ${\ensuremath{\alpha}}_{g}$ being dependent only on the geometric feature of the operation. More interestingly, we demonstrate an experiment to implement a universal set of such kind of generalized unconventional geometric quantum gates with high fidelity in an NMR system.
In a scheme of nonadiabatic purely geometric quantum gates in nuclear-magnetic-resonance systems we propose proper magnitudes of magnetic fields that are suitable for an experiment. We impose a natural condition and reduce the degree of freedom of the magnetic fields to the extent. By varying the magnetic fields with essentially a one-dimensional degree of freedom, any spin state can acquire an arbitrary purely geometric phase ${\ensuremath{\varphi}}_{g}=\ensuremath{-}2\ensuremath{\pi}(1\ensuremath{-}\mathrm{cos}\ensuremath{\theta}),$ $0<~\mathrm{cos}\ensuremath{\theta}<~1.$ This is an essential ingredient for constructing universal geometric quantum gates.
A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single-qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magnetic field parameters, one can let the dynamic phase be proportional to the geometric phase. Then, by controlling the azimuthal angle in the initial state, we may realize a geometric quantum gate whose fidelity is equal to one under cyclic evolution. This means that the quantum information is no distortion in the process of geometric quantum computation.