Stability of holonomic quantum computations

Kuvshinov, V. A.; Kuzmin, A. V.

doi:10.1016/j.physleta.2003.08.011

Cited by 30 publications

(33 citation statements)

References 10 publications

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“…The definition of fidelity is similar with Wilson loop definition in QCD [16]. Using the analogy between the theory of gauge fields and the theory of holonomic quantum computation [2,16,17], we can define the fidelity of quark (the scalar product of state vectors for perturbed and unperturbated motion) as an integral over the closed loop, with particle traveling from point x to the point y:…”

Section: Colour Confinement and Instability Of Colour Particle Motionmentioning

confidence: 99%

Colour particle states behaviour in the QCD vacuum

Kuvshinov

Bagashov

2016

EPJ Web Conf.

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Abstract. The results of an interaction of a quantum state of quark with QCD vacuum, where the latter plays a role of environment, could be treated as decoherence. This may have direct implications for the confinement of quarks phenomenon. The general description and discussion of this process is given. Characteristics from quantum optics and information theory (purity, fidelity, von Neumann entropy) are proposed as means for numerical analysis of the process of interaction of quark colour state with stochastic vacuum. Problems of stability of colour particles motion and order-chaos transitions are briefly discussed. It is shown that there should be a connection between the properties of QCD stochastic vacuum and Higgs boson mass and self interaction coupling constant. The behaviour of squeezed and entangled quantum states, the interaction of colour superpositions and multiparticle states with stochastic QCD vacuum is described. It is shown that it leads to a fully mixed quantum state with equal probabilities for different colours. Decoherence rate is found to be proportional to the product of the distance between colour charges and the time during which this interaction has taken place. I.e. such an interaction seems to lead naturally to confinement of quarks.

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Section: Colour Confinement and Instability Of Colour Particle Motionmentioning

confidence: 99%

Colour particle states behaviour in the QCD vacuum

Kuvshinov

Bagashov

2016

EPJ Web Conf.

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“…The appearance of geometric phases in quantum systems becomes a fundamental feature of the Holonomic Quantum Computation proposed by Zanardy and Raseti in [45]. The implementation of the Holonomic Quantum Computation is based on the using of non-Abelian geometric phases [46][47][48] in such a way that it can achieve great stability [49][50][51][52]. With this motivation, in this work we study the appearance of relativistic and non-relativistic geometric phases in the wave function of a neutral particle with a constant magnetic dipole moment interacting with an external magnetic field in the cosmic string background.…”

Section: Introductionmentioning

confidence: 99%

Scalar Aharonov‐Bohm effect in the presence of a topological defect

Bakke

Furtado²

2010

Annalen der Physik

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In this paper we study the scalar Aharonov-Bohm effect for a neutral particle possessing a magnetic dipole moment in the presence of a cosmic string. We study the phase shift acquired by the wave function of the neutral particle in the presence of this topological defect, investigate this phase shift within nonrelativistic and relativistic quantum descriptions considering two distinct magnetic field configurations and find that the scalar Aharonov-Bohm effect is composed by two contributions, with the first one arises due to the interaction of a magnetic dipole with an external field, and other one arises due to the presence of the cosmic string. The nondispersivity of this effect is also discussed.

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“…Improved insensitivity of HQC to external perturbations is believed to be one of its main advantages, therefore it is important to study the stability of HQC in as general case as possible. Some works on the topic are [5,6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Fidelity of holonomic quantum computations in the case of random errors in the values of control parameters

Buividovich

Kuvshinov

2006

Phys. Rev. A

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We investigate the influence of random errors in external control parameters on the stability of holonomic quantum computation in the case of arbitrary loops and adiabatic connections. A simple expression is obtained for the case of small random uncorrelated errors. Due to universality of mathematical description our results are valid for any physical system which can be described in terms of holonomies. Theoretical results are confirmed by numerical simulations.

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Stability of holonomic quantum computations

Abstract: We study the stability of holonomic quantum computations with respect to errors in assignment of control parameters. The general expression for fidelity is obtaned.In the small errors limit the simple formulae for the fidelity decrease rate is derived.

Cited by 30 publications

References 10 publications

Colour particle states behaviour in the QCD vacuum

Colour particle states behaviour in the QCD vacuum

Scalar Aharonov‐Bohm effect in the presence of a topological defect

Fidelity of holonomic quantum computations in the case of random errors in the values of control parameters

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