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Journal of Physics Condensed Matter

Implementation of a three-qubit refined Deutsch–Jozsa algorithm using SFG quantum logic gates

Andrea Del Duce, Seb J. Savory, Polina Bayvel

Published May 12, 2006• 2 citations
Publisher

Abstract

In this paper we present a quantum logic circuit which can be used for the experimental demonstration of a three-qubit solid state quantum computer based on a recent proposal of optically driven quantum logic gates. In these gates, the entanglement of randomly placed electron spin qubits is manipulated by optical excitation of control electrons. The circuit we describe solves the Deutsch problem with an improved algorithm called the refined Deutsch-Jozsa algorithm. We show that it is possible to select optical pulses that solve the Deutsch problem correctly, and do so without losing quantum information to the control electrons, even though the gate parameters vary substantially from one gate to another. © 2006 IOP Publishing Ltd.

DOI
10.1088/0953-8984/18/21/s07

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In this paper we present a quantum logic circuit which can be used for the experimental demonstration of a three-qubit solid state quantum computer based on a recent proposal of optically driven quantum logic gates. In these gates, the entanglement of randomly placed electron spin qubits is manipulated by optical excitation of control electrons. The circuit we describe solves the Deutsch problem with an improved algorithm called the refined Deutsch-Jozsa algorithm. We show that it is possible to select optical pulses that solve the Deutsch problem correctly, and do so without losing quantum information to the control electrons, even though the gate parameters vary substantially from one gate to another. © 2006 IOP Publishing Ltd.
We analyse the design and optimisation of quantum logic circuits suitable for the experimental demonstration of a three-qubit quantum computation prototype based on optically-controlled, solid-state quantum logic gates. In these gates, the interaction between two qubits carried by the electron-spin of donors is mediated by the optical excitation of a control particle placed in their proximity. First, we use a geometrical approach for analysing the entangling characteristics of these quantum gates. Then, using a genetic programming algorithm, we develop circuits for the refined Deutsch-Jozsa algorithm investigating different strategies for obtaining short total computational times. We test two separate approaches based on using different sets of entangling gates with the shortest possible gate computation time which, however, does not introduce leakage of quantum information to the control particles. The first set exploits fast approximations of controlled-phase gates as entangling gates, while the other one arbitrary entangling gates with a shorter gate computation time compared to the first set. We have identified circuits with consistently shorter total computation times when using controlled-phase gates.
This thesis describes research on the design of quantum logic circuits suitable for the experimental demonstration of a three-qubit quantum computation prototype. The design is based on a proposal for optically controlled, solid-state quantum logic gates. In this proposal, typically referred to as SFG model, the qubits are stored in the electron spin of donors in a solid-state substrate while the interactions between them are mediated through the optical excitation of control particles placed in their proximity. \nAfter a brief introduction to the area of quantum information processing, the basics of quantum information theory required for the understanding of the thesis work are introduced. Then, the literature on existing quantum computation proposals and experimental implementations of quantum computational systems is analysed to identify the main challenges of experimental quantum computation and typical system parameters of quantum computation prototypes. The details of the SFG model are subsequently described and the entangling characteristics of SFG two-qubit quantum gates are analysed by means of a geometrical approach, in order to understand what entangling gates would be available when designing circuits based on this proposal. Two numerical tools have been developed in the course of the research. These are a quantum logic simulator and an automated quantum circuit design algorithm based on a genetic programming approach. Both of these are used to design quantum logic circuits compatible with the SFG model for a three-qubit Deutsch-Jozsa algorithm. One of the design aims is to realise the shortest possible circuits in order to reduce the possibility of errors accumulating during computation, and different design procedures which have been tested are presented. The tolerance to perturbations of one of the designed circuits is then analysed by evaluating its performance under increasing fluctuations on some of the parameters relevant in the dynamics of SFG gates. Because interactions in SFG two-qubit quantum gates are mediated by the optical excitation of the control particles, the solutions for the generation of the optical control signal required for the proposed quantum circuits are discussed. Finally, the conclusions of this work are presented and areas for further research are identified.
We analyze the preparation of an experimental demonstration for a three-qubit, optically controlled, solid-state quantum computational system. First, using a genetic programming approach, we design quantum logic circuits, specifically tailored for our computational model, which implement a three-qubit refined Deutsch-Jozsa algorithm. Aiming at achieving the shortest possible computational time, we compare two design strategies based on exploiting two different sets of entangling gates. The first set comprises fast approximations of controlled-phase gates, while in the second case, we exploit arbitrary entangling gates with gate computational times shorter than those of the first set. Then, considering some recently proposed material implementations of this quantum computational system, we discuss the generation of the near-midinfrared, multiwavelength and picosecond optical pulse sequences necessary for controlling the presented quantum logic circuits. Finally, we analyze potential sources of errors and assess the impact of random fluctuations of the parameters controlling the entangling gates on the overall quantum computational system performance.
We propose a way to implement a three-qubit refined Deutsh-Jozsa (DJ) algorithm. The present proposal is based on the construction of the 35 fff-controlled phase gates, which uses single-qubit σzσ_zσz​ gates and two-qubit {\it standard} controlled-phase (CP) gates only. This proposal is implementable because a single-qubit σzσ_zσz​ gate can be easily realized by applying a single classical pulse and a two-qubit CP gate has been experimentally demonstrated in various physical systems. Finally, it is noted that this proposal is quite general, and can be applied to implement a three-qubit refined DJ algorithm in a cavity-based or noncavity-based physical system.
Abstract In efforts toward the realization of quantum computers, there have been many proposals to implement controlled NOT gates between quantum bits (qubits). However, the number of quanta in the experimentally realized system has been at most two. Because it is difficult to cope with both the realization of the conditional interaction (e.g., huge nonlinear interaction) between the quanta, and the maintenance of quantum coherence for a sufficient time, the realization of quantum logic gates using several quanta may be difficult in the near future. In this paper, a new method which implements a quantum algorithm using linear optics and single photons is described. This method does not need any huge nonlinearity. Hence, it is practical with today's technology and will be one of the useful physical test beds for the quantum algorithms. The optical implementation of the Deutsch–Jozsa algorithm with a 4‐bit input is proposed, and the mechanism is explained. As one instance of the recent progress of our project, an experiment of single‐photon interference using parametric fluorescence with highly stabilized interferometer system is reported. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(11): 52–60, 2001