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arXiv:quant-ph/0304174 · Chinese Physics Letters

Universal Quantum Gates Based on Both Geometric and Dynamic Phases in Quantum Dots

Kaiyu Yang, Shi-Liang Zhu, Wang Zi-Dan

Published Jun 17, 2003• 11 citations
arXivHTMLPDF

Abstract

A large-scalable quantum computer model, whose qubits are represented by the subspace subtended by the ground state and the single exciton state on semiconductor quantum dots, is proposed. A universal set of quantum gates in this system may be achieved by a mixed approach, composed of dynamic evolution and nonadiabatic geometric phase.
DOI
10.1088/0256-307x/20/7/306

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Abstract Using the analytic expression of the evolution operator for the electron spin in a quantum dot, we propose a scheme to design a universal set of single‐qubit gates based solely on the geometric phase that the qubit state acquires after a cyclic evolution in the parameter space. The scheme is using ultrafast linearly chirped pulses providing adiabatic excitation of the qubit states and the geometric phase is fully controlled by the relative phase between pulses. © 2012 Wiley Periodicals, Inc.
In the last decade, a lot of effort have gone to find the most appropriate physical implementation of quantum computer. Quantum dot based system is one of the most promising system owing to its integrability with classical computation hardware and its versatility in realizing qubits and quantum gates. In this work, we propose a model for quantum dot based realization of qubits and quantum gates. The proposed system makes use of semiconductor hetrostructure based quantum dots and gate voltages to confine electrons and thus defining the qubits. Electron spin resonance is used to manipulate the spin state of the electrons. We implement single, double and triple qubit systems and two most widely used universal sets of quantum gates. We show full control of Bloch sphere in single qubit system, CNOT gate implementation in double qubit system and a novel way to implement Toffoli gate in triple qubit system.
We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.
We propose a scheme for realizing the scalable quantum computation based on nonidentical quantum dots trapped in a single-mode waveguide. In this system, the quantum dots simultaneously interact with a large detuned waveguide and classical light fields. During the process, neither the waveguide mode nor the quantum dots are excited, while the sub-system composed of any two quantum dots can acquire phases conditional upon the states of these two quantum dots and the certain detunings between the waveguide mode and corresponding external light fields. Therefore, it can be used to realize selective quantum phase gates, graph states, NNN-qubit controlled phase πππ gates, and cluster states.