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arXiv:quant-ph/0301089 · Physical Review A

Nonadiabatic geometrical quantum gates in semiconductor quantum dots

Paolo Solinas, Paolo Zanardi A, Nino Zanghı̀, Fausto Rossi

Published May 23, 2003• 57 citations
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Abstract

In this paper, we study the implementation of nonadiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding (manipulation) schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase, one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be, in principle, implemented.

DOI
10.1103/physreva.67.052309

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In this paper, we study the implementation of nonadiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding (manipulation) schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase, one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be, in principle, implemented.
Recently, geometric phases, which is fault tolerate to certain errors intrinsically due to its geometric property, are getting considerable attention in quantum computing theoretically. So far, only one experiment about adiabatic geometric gate with NMR through Berry phase has been reported. However, there are two drawbacks in it. First, the adiabatic condition of Berry phase makes such gate very slowly. Second, the extra operation to eliminate the dynamic phase. As we know, geometric phase can exist both adiabatic(Berry phase) and nonadiabatic(Aharonov-Anandan phase). In this letter, we reports the first experimental realization of nonadiabatic geometric gate with NMR through conditional-AA phase. In our experiment the gates can be made faster and more easily, and the two drawbacks mentioned above are removed.
We propose an implementation scheme for holonomic, i.e., geometrical, quantum information processing based on semiconductor nanostructures. Our quantum hardware consists of coupled semiconductor macroatoms addressed/controlled by ultrafast multicolor laser-pulse sequences. More specifically, logical qubits are encoded in excitonic states with different spin polarizations and manipulated by adiabatic time control of the laser amplitudes. The two-qubit gate is realized in a geometric fashion by exploiting dipole-dipole coupling between excitons in neighboring quantum dots.
A review of semiconductor-based schemes for the realization of quantum information processing devices is presented. After recalling the fundamentals of quantum information/computation theory, we shall discuss potential implementation schemes based on charge and/or spin degrees of freedom in semiconductor nanostructures. More specifically, we shall present an all-optical implementation scheme of quantum information processing with semiconductor macroatoms/molecules, where the computational degrees of freedom are interband optical transitions (excitonic states) manipulated/controlled by ultrafast sequences of multicolor laser pulses. We shall primarily focus on implementation schemes dealing with charge excitations in GaAs as well as GaN quasi-zero-dimensional structures. We shall finally discuss the possibility to combine charge and spin degrees of freedom, thus, allowing for fast-quantum gates, which do not translate into fast-decoherence times.
A review of semiconductor-based schemes for the realization of quantum information processing devices is presented. After recalling the fundamentals of quantum information/computation theory, we shall discuss potential implementation schemes based on charge and/or spin degrees of freedom in semiconductor nanostructures. More specifically, we shall present an all-optical implementation scheme of quantum information processing with semiconductor macroatoms/molecules, where the computational degrees of freedom are interband optical transitions (excitonic states) manipulated/controlled by ultrafast sequences of multicolor laser pulses. We shall primarily focus on implementation schemes dealing with charge excitations in GaAs as well as GaN quasi-zero-dimensional structures. We shall finally discuss the possibility to combine charge and spin degrees of freedom, thus allowing for fast quantum gates which do not translate into fast decoherence times.
We introduce the nonadiabatic, or Aharonov-Anandan, geometric phase as a tool for quantum computation and show how this phase on one qubit can be monitored by a second qubit without any dynamical contribution. We also discuss how this geometric phase could be implemented with superconducting charge qubits. While the nonadiabatic geometric phase may circumvent many of the drawbacks related to the adiabatic (Berry) version of geometric gates, we show that the effect of fluctuations of the control parameters on nonadiabatic phase gates is more severe than for the standard dynamic gates. Similarly, fluctuations also affect to a greater extent quantum gates that use the Berry phase instead of the dynamic phase.