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Communications in Theoretical Physics

Implementation of Quantum Fourier Transform and Its Applications via Quantum-Dot Spins and Microcavity

Dong Ping, Zheng Xiao-Hu, Zhang Gang, Zhuo‐Liang Cao

Published Sep 1, 2009• 0 citations
Publisher

Abstract

A scheme for implementing discrete quantum Fourier transform is proposed via quantum dots embedded in a microcavity, and then some of its applications are investigated, i.e., Deutsch–Jozsa algorithm and Shor's quantum factoring. In particular, the detailed process of implementing one-qubit Deutsch–Jozsa algorithm and the factorization of N = 15 are given. The microcavity mode is only virtually excited in the whole interaction, so the effective decoherent has slight effect on the current scheme. These schemes would be an important step to fabricate a solid quantum computer.

DOI
10.1088/0253-6102/52/3/09

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A scheme for implementing discrete quantum Fourier transform is proposed via quantum dots embedded in a microcavity, and then some of its applications are investigated, i.e., Deutsch–Jozsa algorithm and Shor's quantum factoring. In particular, the detailed process of implementing one-qubit Deutsch–Jozsa algorithm and the factorization of N = 15 are given. The microcavity mode is only virtually excited in the whole interaction, so the effective decoherent has slight effect on the current scheme. These schemes would be an important step to fabricate a solid quantum computer.
In this paper, we briefly review the basic concepts of quantum computation, entanglement, quantum cryptography and quantum fourier transform. Quantum algorithms like Deutsch Jozsa, Shor’s factorization and Grover’s data search are developed using fourier transform and quantum computation concepts to build quantum computers. Researchers are finding a way to build quantum computer that works more efficiently than classical computer. Among the standard well known algorithms in the field of quantum computation and communication we describe mathematically Deutsch Jozsa algorithm in detail for 2 and 3 qubits. Calculation of balanced and unbalanced states is shown in the mathematical description of the algorithm.
A scheme for the implementation of the two-qubit Deutsch-Jozsa algorithm using cavity QED was proposed.The advantages of the proposal are demonstrated as follows.One is that the cavity feld is only virtually excited and the photon-number-dependent part in the effective Hamiltonian is cancelled so that the system is insensitive to the cavity decay and the thermal field.The other one is that we don't require any Hadamard operation,which makes the schematic setup simple.Therefore,the present scheme is available based on the current technologies.
We propose two physical schemes for implementing the simplest version of Deutsch-Jozsa algorithm(D-J) based on cavity QED technique.One is a perfect scheme,which can be generalized to multi-qubit inputs Deutsch-Jozsa algorithm.It can be realized with the help of controlled-NOT gates and single-qubit operations.The detailed process in cavity QED is discussed in the scheme.The other is a simpler scheme without controlled-NOT gates,which is only suit for the simplest version of Deutsch-Jozsa algorithm.The scheme only requires single-qubit operation.Thus the scheme can be realized easier than the former one.Our schemes would be an important step for quantum computer.
A new physical scheme for implementing an N-bit discrete quantum Fourier transform (DQFT) is proposed via superconducting (SC) qubits coupled to a single-mode SC cavity. Two-qubit and one-qubit gates as well as a new two-qubit gate are realized. Such gates are used for implementing the algorithm of N-bit DQFT. We propose and analyze a detailed experimental procedure for implementing the algorithm and compute the fidelity measure to quantify the success of this algorithm. Estimates show that the protocol can be successfully implemented within the present experimental limits.