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arXiv:1307.1375 · Journal of the Physical Society of Japan

Proposal for Implementing the Three-Qubit Refined Deutsch–Jozsa Quantum Algorithm

Qi-Ping Su, Man Liu, Chui-Ping Yang

Published Jul 12, 2013• 0 citations
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Abstract

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 $f$-controlled phase gates, which uses single-qubit $σ_z$ gates and two-qubit {\it standard} controlled-phase (CP) gates only. This proposal is implementable because a single-qubit $σ_z$ 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.

DOI
10.7566/jpsj.82.084802

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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.
We theoretically study the realization of a multi-qubit refined Deutsch-Jozsa (DJ) algorithm using resonant interaction of many Rydberg atoms with a single-mode microwave cavity, in which the multi-qubit controlled phase gates could be accomplished efficiently. We show how to achieve a multi-qubit refined DJ algorithm in high fidelity, even in the case of a weak cavity decay and some imperfection. We argue that the required operations in our scheme are almost within the present experimental possibilities.
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.
We propose a way to realize a multiqubit controlled-phase gate with one qubit simultaneously controlling n target qubits using atoms in cavity QED. In this proposal, there is no need to use classical pulses during the entire gate operation. The gate operation time scales as |n\sqrt {n}n​| only and thus the gate can be performed faster when compared with sending atoms through the cavity one at a time. In addition, only three operational steps are required to realize this n-target-qubit controlled-phase gate. This proposal is quite general and can be applied to other physical systems, such as various superconducting qubits coupled to a resonator, NV centers coupled to a microsphere cavity, or quantum dots in cavity QED.
基于联合到一个洞的超导的量干扰设备(枪乌) ，我们为实现一扇量控制阶段门(QPG ) 和 Deutsch-Jozsa (DJ ) 建议一个计划由一个可控制的相互作用的算法。作为量数据公共汽车在现在的计划，在费用政体的 SQUID 工作，和洞地是 ultilized，它顺序一次被联合到仅仅一 qubit。在选择 qubit 和数据公共汽车之间的相互作用例如反响、散的相互作用，能被 SQUID.Especially 转各个的门电容认识到，公共汽车没激动，因此，洞腐烂在 DJ 的实现期间被压制算法。为 QPG 操作，公共汽车的模式操作最后是未改变的，尽管它的模式确实在操作期间激动。为典型实验数据，最后，我们简单地分析建议计划的试验性的可行性。基于简单操作，我们的计划可以在这被认识到固态系统，和我们的想法可以在另外的系统被认识到。
A scheme to execute an \\eta-bit Deutsch-Jozsa (DJ) algorithm using \\eta qubits has been implemented for up to three qubits on an NMR quantum computer. For the one- and the two-bit Deutsch problem, the qubits do not get entangled, and the NMR implementation is achieved without using spin-spin interactions. It is for the three-bit case, that the manipulation of entangled states becomes essential. The interactions through scalar J-couplings in NMR spin systems have been exploited to implement entangling transformations required for the three bit DJ algorithm.