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Quantum Information and Computation

Geometric phase carried by the observables and its application to quantum computation

WangZisheng, PanHui

Published Sep 1, 2015• 0 citations
Publisher

Abstract

We investigate geometric phases in terms of Heisenberg equation. We find that, equivalently to Schrodinger picture with a memory of its motion in terms of the geometric phase factor contained in th...
DOI
10.5555/2871350.2871355

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Geometric phase carried by the observables and its application to quantum computation

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We investigate geometric phases in terms of Heisenberg equation. We find that, equivalently to Schr\"odinger picture with a memory of its motion in terms of the geometric phase factor contained in the wave function, the observales carry with the geometric message under their evolutions in the Heisenberg picture. Such an intrinsic geometric feature may be particularly useful to implement the multi-time correlation geometric quantum gate in terms of the observables, which leads to a possible reduction in experimental errors as well as gate timing. An application is discussed for nuclear-magnetic-resonance system, where the geometric quantum gate is proposed.

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We investigate geometric phases in terms of Heisenberg equation. We find that, equivalently to Schr\"odinger picture with a memory of its motion in terms of the geometric phase factor contained in the wave function, the observales carry with the geometric message under their evolutions in the Heisenberg picture. Such an intrinsic geometric feature may be particularly useful to implement the multi-time correlation geometric quantum gate in terms of the observables, which leads to a possible reduction in experimental errors as well as gate timing. An application is discussed for nuclear-magnetic-resonance system, where the geometric quantum gate is proposed.
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By using group representation theory, th quasi-adiabatic approximation solution of the schrodinger equation of a quantum system with slowly-changing Hamiltonian are presented in this paper. We not only obtained the Berry phase factor and strictly proved the quantum adiabatic theorem as the zeroth-order approximation, but also studied the universal Berry phase factor and its geometrical interpretation when the adiabatic condition is violated. It is pointed out that this universal Berry phase factor has observable effects.
Abstract We present an exact quantum observable analog of the weak equivalence principle for a ‘relativistic’ quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as p µ , rather than p µ . We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation.