利用仲氢诱导极化技术实现 Deutsch算法

核磁共振系统是实现量子计算的有效物理体系之一．但是随着量子位数的不断增加,运用核磁共振技术实现计算任务存在明显的局限性,原因之一是量子计算的初始态-赝纯态,随着量子位数的增加,信号指数性的衰减,量子位数越多制备赝纯态所需的脉冲序列越复杂,越不容易实现,不利于量子位数的扩展;另外,由于核磁共振中制备的赝纯态实际上也是一种混合态,用于实现量子信息任务时存在一定的争议．该文介绍的利用仲氢诱导极化技术(PHIP)制备出的实验初态,能够解决初态处于混合态的问题,并且信号强度显著增强,作者利用此态实现了 ALTADENA 条件下的两量子位的 Deutsch-Jozsa 量子算法和 PASADENA 条件下的三量子位的Deutsch-Like 量子算法．
     

Implementation of the Deutsch-Jozsa algorithm violates nonlocal realism

The theoretical resource state for the implementation of the Deutsch-Jozsa algorithm is a multiqubit pure uncorrelated state. We show that N-qubit pure uncorrelated quantum states cannot admit rotationally invariant nonlocal realistic theories with a violation factor of 3^N. We find the violation factor 3^Nwhen the measurement setup is entire range of settings for each of the observers, that is, considering rotationally invariant nonlocal realistic theories along with the property of a correlation function in the quantum theory. The implementation of the Deutsch-Jozsa algorithm theoretically relying on N-qubit pure uncorrelated states rules out rotationally invariant nonlocal realism with a violation factor of 3^Nin an ideal case. Our analysis relies on the property of theoretical resource states for the algorithm. We cannot simulate the Deutsch-Jozsa algorithm by using rotationally invariant nonlocal realistic theories due to the property of theoretical resource states for the algorithm.     

Preparing high purity initial states for nuclear magnetic resonance quantum computing

Here we demonstrate how parahydrogen can be used to prepare a two-spin system in an almost pure state which is suitable for implementing nuclear magnetic resonance quantum computation. A 12 ns laser pulse is used to initiate a chemical reaction involving pure parahydrogen (the nuclear spin singlet of H2). The product, formed on the micros time scale, contains a hydrogen-derived two-spin system with an effective spin-state purity of 0.916. To achieve a comparable result by direct cooling would require an unmanageable (in the liquid state) temperature of 6.4 mK or an impractical magnetic field of 0.45 MT at room temperature. The resulting spin state has an entanglement of formation of 0.822 and cannot be described by local hidden variable models.     

Use of non-adiabatic geometric phase for quantum computing by NMR

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.     

七量子位Deutsch-Josza量子算法的核磁共振实验实现

近年来 ,量子计算机的研究有了很大的发展 ,在目前提出的各种量子计算的方案中 ,核磁共振技术对模拟和演示量子算法以及验证量子计算机的优越性做出了巨大的贡献 .Deutsch Jozsa算法是一种研究较为广泛的量子算法 ,它可以用核磁共振实验予以验证 ,并可根据Cirac等人提出的方案予以简化 .报道了在核磁共振量子计算机上实验实现七位Deutsch Jozsa算法的过程和结果. Recent years, remarkable progresses in experimental realization of quantum information have been made, especially based on nuclear magnetic resonance (NMR) theory. In all quantum algorithms, Deutsch-Jozsa algorithm has been widely studied. It can be realized on NMR quantum computer and also can be simplified by using the Cirac s scheme. In this paper, at first the principle of Deutsch-Jozsa quantum algorithm is analyzed, then we implement the seven-qubit Deutsch-Jozsa algorithm...     

经典混沌系统在相应于初始相干态的量子子空间中的随机性

Poincare截面是反映经典系统是否达到混沌的有力手段,无规矩阵理论被看成是显示量子系统规则运动与不规则运动特征的有效方法．那么,当一个经典相点在混沌体系的某一能量面E₀上的不变环面被全部破坏后,与这一相点所对应的中心能量E₀等于E₀的相干态波包在它所占据的量子系统的子空间中有何表现呢？以原子核Lipkin模型为例,用重整化约化方法,对SU（3）群的广义相干态所占据的量子子空间进行了约化后对其中有关量的随机性作了考察,结果表明,在这样的等效子空间内能级间距的涨落,等效哈密顿量的矩阵元以及从可积体系的子空间到这一等效子空间的一一映射的矩阵元的分布均与无规矩阵理论的预言相符合,从而为进一步研究经典部分可积体系的量子表现奠定了基础. 关键词：     

Pairwise entanglement in symmetric multi-qubit systems

For pairs of particles extracted from a symmetric state of N two-level systems, the two-particle density matrix is expressed in terms of expectation values of collective spin operators for the large system. Results are presented for experimentally relevant examples of pure states: Dicke states | S, M>, spin coherent, and spin squeezed states, where only the symmetric subspace, S = N/2 is populated, and for thermally entangled mixed states populating also lower S values. The entanglement of the extracted pair is then quantified by a calculation of the concurrence, which provides directly the entanglement of formation of the pair. Received 9 May 2001 and Received in final form 16 November 2001     

Nonadiabatic Geometric Phase in Composite Systems and Its Subsystem

We point out that the time-dependent gauge transformation technique may be effective in investigating the nonadiabatic geometric phase of a subsystem in a composite system. As an example, we consider two uniaxially coupled spin -1/2 particles with one of particles driven by rotating magnetic field. The influences of coupling and precession frequency of the magnetic field on geometric phase are also discussed in detail.     

Implementing logic gates and the Deutsch-Jozsa quantum algorithm by two-dimensional NMR using spin- and transition-selective pulses

Quantum logical operations using two-dimensional NMR have recently been described using the scalar coupling evolution technique [J. Chem. Phys. 109, 10603 (1998)]. In the present paper, we describe the implementation of quantum logical operations using two-dimensional NMR, with the help of spin- and transition-selective pulses. A number of logic gates are implemented using two and three qubits with one extra observer spin. Some many-in-one gates (or Portmanteau gates) are also implemented. Toffoli gate (or AND/NAND gate) and OR/NOR gates are implemented on three qubits. The Deutsch-Jozsa quantum algorithm for one and two qubits, using one extra work qubit, has also been implemented using spin- and transition-selective pulses after creating a coherent superposition state in the two-dimensional methodology.     

The Elusive Source of Quantum Speedup

We discuss two qualities of quantum systems: various correlations existing between their subsystems and the distinguishability of different quantum states. This is then applied to analysing quantum information processing. While quantum correlations, or entanglement, are clearly of paramount importance for efficient pure state manipulations, mixed states present a much richer arena and reveal a more subtle interplay between correlations and distinguishability. The current work explores a number of issues related with identifying the important ingredients needed for quantum information processing. We discuss the Deutsch-Jozsa algorithm, the Shor algorithm, the Grover algorithm and the power of a single qubit class of algorithms. In the latter, a quantity called discord is seen to be more important than entanglement. One section is dedicated to cluster states where entanglement is crucial, but its precise role is highly counter-intuitive. Here we see that the notion of distinguishability becomes a more useful concept.