超导量子比特网络实现Deutsch-Jozsa算法

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"基于超导量子比特网络的Deutsch-Jozsa算法实现方案" 这篇由郑小虎、Ming Yang和Ping Dong等人提出的论文是关于在超导量子比特网络中实施Deutsch-Jozsa算法的研究成果，它属于"首发论文"类别。文章中提到的一个关键改进是通过电流偏置实现普适逻辑门的结构，这一改进对于构建功能强大且可扩展的量子计算机至关重要。当前的技术已经具备制造这种架构的能力。 Deutsch-Jozsa算法是量子计算中的一个重要算法，由物理学家David Deutsch和Richard Jozsa于1992年提出。该算法旨在解决一个特定的决策问题：判断一个未知的黑箱函数是否是平衡的或常数的。在经典计算中，这可能需要查询函数多次才能确定，但量子计算机可以一次性解决这个问题，体现出量子计算的优越性。超导材料因其超低的电阻和电容，成为了实现量子比特的理想选择。 Josephson charge qubits（约瑟夫森电荷量子比特）是超导量子计算中的基本单元，它们利用Josephson结的非线性电动力学特性来编码和操纵量子信息。论文中提出的改进结构通过电流控制这些量子比特，实现了通用逻辑门的执行，从而为量子计算提供更高效的操作平台。文章还研究了如何在这个改进的架构上实现Deutsch-Jozsa算法。他们提出的方法简单、可扩展并且可行，基于当前受控的超导电荷量子比特网络。这一方案不仅有助于验证量子计算机的理论，也为实际应用奠定了基础。 PACS号码03.67.Lx和85.25.Cp分别对应量子力学的量子信息处理和超导物理学领域。关键词包括Deutsch-Jozsa算法、超导性和Josephson电荷量子比特，强调了该研究的核心内容——量子叠加状态和纠缠性质如何赋予量子计算机超越传统计算机的强大计算潜力。这篇论文对量子计算领域的贡献在于提出了一种新的超导量子比特网络结构，用于执行Deutsch-Jozsa算法，这一进展有望推动量子计算技术的发展，尤其是在实现大规模量子计算系统方面。

Implementing Deutsch-Jozsa algorithm using superconducting qubit network

Xiao-Hu Zheng

∗

Ming Yang,

Ping Dong,

and Zhuo-Liang Cao

†1

Key Laboratory of Opto-electronic Information Acquisition and Manipulation, Ministry of Education,

School of Physics and Material Science, Anhui University, Hefei, 230039, P R China

An improved architecture, which perform a universal set of gates by current biasing of coupling Josephson

junction, has been proposed. This improvement is necessary to the realization of a functional and scalable quan-

tum computer. The proposed architecture is in line with current technology. Secondly, we investigate a scheme

for implementing Deutsch-Jozsa algorithm via the improved architecture. It is a simple, scalable and feasi-

ble scheme for the implementation of Deutsch-Jozsa algorithm based on the current-controlled superconducing

charge qubit network.

PACS numbers: 03.67.Lx, 85.25.Cp

Keywords: Deutsch-Jozsa algorithm; Superconduction; Josephson charge qubits

Superposition principle of quantum state and entanglement

property make quantum computers possess potentially supe-

rior computing power over their classical counterparts, which

is demonstrated by some Quantum algorithms. Shor’s al-

gorithm [1] can be used to quickly factorize large numbers.

Grover search algorithm is fairly efﬁcient in looking for one

item in an unsorted database of size N ≡ 2

[2, 3]. The

Deutsch-Jozsa (DJ) algorithm[4] is one of the simple quan-

tum algorithm which provides an exponential speed-up with

respect to classical algorithms. In this paper, we focus the DJ

algorithm.

The DJ algorithm can be brieﬂy described as follows: As-

sume a Boolean functions f : {0, 1}

→ {0, 1}. If the func-

tion values are only single 0 or 1 for all 2

inputs, the func-

tion is called constant. If the function values are equal to 1

for half of all possible inputs, and to 0 for the other half, the

function is called balanced. The DJ algorithm is designed to

distinguish whether a function f is constant or balanced. With

a classical algorithm, this problem would, in the worst case,

require (2

N−1

+ 1) queries of f whereas the DJ algorithm re-

quires only one query by means of the following steps[5, 6],

as shown Fig. 1 (here we eliminate a 1-qubit function register

which is used for storing the function values , while retain an

N-qubit control register for the function arguments).

(i) N qubits are prepared in the initial state |00 . . . 0i.

(ii) Perform an N-qubit Hadamard transformation H

(iii) Apply the f-controlled phase shift U

|xi

−→ (−1)

f(x)

|xi , (x ∈ {0, 1}

) . (1)

(iv) Perform another Hadamard transformation H.

(v) Measure the ﬁnal state. If the result is |00 . . . 0i the

function f is constant; if, however, the amplitude a

|00...0i

the state |00 . . . 0i is zero the function f is balanced. This is

because

|00...0i

x∈{0,1}

(−1)

f(x)

. (2)

∗

Electronic address: xhzheng@ahu.edu.cn

†

Electronic address:zlcao@ahu.edu.cn (Corresponding Author)

measure

final state

prepare

Initial state

H H

FIG. 1: Schematic diagram of the Deutsch-Jozsa

For realizing quantum computers, some physical systems,

such as nuclear magnetic resonance [7], trapped irons [8],

cavity quantum electrodynamics (QED) [9], and optical sys-

tems [10] have been proposed. These systems have the ad-

vantage of high quantum coherence, but can’t be integrated

easily to form large-scale circuits. Because of large-scale in-

tegration and relatively high quantum coherence, Josephson

charge qubit [11–13] and ﬂux qubit [14, 15], which are based

on the macroscopic quantum effects in superconducting cir-

cuits [16, 17], are the promising candidates for quantum com-

puting. The DJ algorithm has special functions, so the imple-

mentation of DJ algorithm has become the focus of research.

For example, the DJ algorithm has been implemented with

pure coherent molecular superpositions [18], with quantum

dot [19, 20], and with cavity QED [21]. In this paper, we pro-

pose a physical scheme for implementing the DJ algorithm

with superconducting qubit network. It is a simple, scalable

and feasible scheme for implementing the DJ algorithm.

The paper is organized as follows: Firstly, we introduce

the structure and Hamiltonian of the current-controlled su-

perconducing charge qubit network. Secondly, we explain

how to implement a universal set of gates with this network.

Thirdly, we review the advantages, the decoherence feature

and extendability of the superconducting charge qubit net-

work. Fourthly, we illustrate the implementation of the DJ

algorithm. Finally, the conclusions are given.

Since the earliest Josephson charge qubit scheme [11] was

proposed, a series of improved schemes [12, 22, 23] have

been explored. Here, basing on the architecture of Joseph-

son charge qubit in Ref. [23], we propose an improved

architecture. The superconducting charge qubits structure

is shown in Fig.2. All N charge qubits (Q

, Q

, . . . , Q

)

can interact with the charge qubit Q

by a common large-

http://www.paper.edu.cn

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