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.     

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...     

Liquid Nuclear Magnetic Resonance Implementation of Quantum Computation in Subspace

Based on the logical labelling method, we prepare an effective pure state in a subsystem of a three spin system via liquid nuclear magnetic resonance technique. Then with this subspace effective pure state we implement the Deutsch-Jozsa algorithm. The tomography for the subspace effective pure state and the corresponding spectrum of the output for the Deutsch-Jozsa algorithm agree with theoretical predictions, which shows that we have successfully implemented the Deutsch-Jozsa algorithm in a subsystem of a nuclear spin system and demonstrated a subspace quantum computation.     

Can von Neumann’s Theory Meet the Deutsch-Jozsa Algorithm?

The theoretical formalism of the implementation of the Deutsch-Jozsa algorithm relies on von Neumann’s theory. We try to investigate whether von Neumann’s theory meet our physical world. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1≤N<+∞). This assumption intuitively depictures our physical world. However, the quantum predictions within the formalism of von Neumann’s projective measurement violate the proposition with a magnitude that grows exponentially with the number of particles. Therefore, von Neumann’s theory cannot depicture our physical world with a violation factor that grows exponentially with the number of particles. Hence, von Neumann’s theory cannot meet the Deutsch-Jozsa algorithm. We propose the solution of the problem. Our solution is equivalent to changing Planck’s constant (?) to new constant (\(\hbar/\sqrt{2}\)). It may be that a new type of the quantum theory early approaches Newton’s theory in the macroscopic scale than the old quantum theory does so.     

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

A scheme for implementing discrete quantum Fourier transform isproposed via quantum dots embedded in a microcavity, and then someof 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 schemeswould be an important step to fabricate a solid quantum computer.     

实现D-J量子算法的物理方案

利用腔QED技术,我们在本文提出了两个物理方案用来实现最简单版本的Deutsch-Jozsa(D-J)量子算法.第一个方案是比较理想的方案,这个方案可以推广到多个量子比特输入的Deutsch-Jozsa量子算法.我们只需要通过实现控制-非门和一系列单个量子比特操作,就可以简单的实现该方案.我们在这个方案中详细地讨论了基于腔QED技术最简单版本的Deutsch-Jozsa量子算法的实现过程.另一个方案是不需要控制-非门的更简单的方案,但是这个方案仅仅适用于实现这种最简单版本的Deutsch-Jozsa量子算法,这个方案只需要实现单个量子比特操作即可.显然,该方案比第一个方案更简化.我们的这两个方案可能是实现量子计算机的一个重要环节.     

Quantum entanglement in the NMR implementation of the Deutsch-Jozsa algorithm

A scheme to execute an n-bit Deutsch-Jozsa (DJ) algorithm using n 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.     

Quantum-classical correspondence and nonclassical state generation in dissipative quantum optical systems

We develop a semiclassical method to determine the nonlinear dynamics of dissipative quantum optical systems in the limit of large number of photons N; it is based on the 1/N-expansion and the quantum-classical correspondence. The method is used to tackle two problems: the study of the dynamics of nonclassical state generation in higher order anharmonic dissipative oscillators and the establishment of the difference between the quantum and classical dynamics of the second-harmonic generation in a self-pulsing regime. In addressing the first problem, we obtain an explicit time dependence of the squeezing and the Fano factor for an arbitrary degree of anharmonism in the short-time approximation. For the second problem, we analytically find a characteristic time scale at which the quantum dynamics differs insignificantly from the classical one.     

Implementtion of a Computation Algorithm for Deutsch-Jozsa Problem Utilizing Spatial Distribution of Photons

Several implementations of quantum computation making effective use of the quantum behavior of single-photons have been explored. These implementing methods were found unsuitble for large-scale computation, because they require 2^N-1 optical paths to represent N qubits. In this paper, a new computing scheme is described which utilizes spatial distribution of photons. The occupation of several optical paths by single-photons is adopted as qubits. This adoption gives several extension of processing capacity and computational functionality with a simple setup. An optical implementation of a solution algorithm on four-bit Deutsch-Jozsa problem is demonstrated with utilization of the spatial distribution of photons.     

Disorder-induced quantum-Griffiths-like features from a non-conventional renormalization group analysis near four dimensions

We investigate the role played by symmetry conserving quenched disorder on quantum criticality of a variety of d-dimensional systems with a continuous symmetry order parameter. We employ a non-standard procedure which combines a preliminary reduction to an effective classical random problem and a successive conventional renormalization group treatment. Solving the effective flow equations to first order in ε=4−d and then restoring the original coupling parameters, for d<4 we find a quantum critical point scenario exhibiting unusual features, which remind us of some predictions of the quantum Griffiths phase model.     

Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm

For a practical quantum computer to operate, it is essential to properly manage decoherence. One important technique for doing this is the use of "decoherence-free subspaces" (DFSs), which have recently been demonstrated. Here we present the first use of DFSs to improve the performance of a quantum algorithm. An optical implementation of the Deutsch-Jozsa algorithm can be made insensitive to a particular class of phase noise by encoding information in the appropriate subspaces; we observe a reduction of the error rate from 35% to 7%, essentially its value in the absence of noise.     

Quantum computation in continuous time using dynamic invariants

We introduce an approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain conditions, for the design of quantum algorithms running on a nonadiabatic regime. We show that the relaxation of adiabaticity can be achieved by processing information in the eigenlevels of a time dependent observable, namely, the dynamic invariant operator. Moreover, we derive the conditions for which the computation can be implemented by time independent as well as by adiabatically varying Hamiltonians. We illustrate our results by providing the implementation of both Deutsch-Jozsa and Grover algorithms via dynamic invariants.     

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.     

Quantum information processing with delocalized qubits under global control

Conventional quantum computing schemes are incompatible with nanometer-scale "hardware," where the closely packed spins cannot be individually controlled. We report the first experimental demonstration of a global control paradigm: logical qubits delocalize along a spin chain and are addressed via the two terminal spins. Using NMR studies on a three-spin molecule, we implement a globally clocked quantum mirror that outperforms the equivalent swap network. We then extend the protocol to support dense qubit storage and demonstrate this experimentally via Deutsch and Deutsch-Jozsa algorithms.     

A Generalization of Schur–Weyl Duality with Applications in Quantum Estimation

Schur–Weyl duality is a powerful tool in representation theory which has many applications to quantum information theory. We provide a generalization of this duality and demonstrate some of its applications. In particular, we use it to develop a general framework for the study of a family of quantum estimation problems wherein one is given n copies of an unknown quantum state according to some prior and the goal is to estimate certain parameters of the given state. In particular, we are interested to know whether collective measurements are useful and if so to find an upper bound on the amount of entanglement which is required to achieve the optimal estimation. In the case of pure states, we show that commutativity of the set of observables that define the estimation problem implies the sufficiency of unentangled measurements.     

Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits

We report on a fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms for 8-point functions. The measured visibility of the 8-path interferometer is about 97.5%. Potential applications of our setup to quantum communication or cryptographic protocols using several qubits are discussed.     

Thermal activation rates in the chirally asymmetric Gross-Neveu model

We address the problem of how to incorporate quantum effects into the calculation of finite-temperature decay rates for a metastable state of a quantum field theory. To do this, we consider the Gross-Neveu model with an explicit chiral symmetry breaking term, which allows for a metastable state. This theory can be shown to have a “critical bubble” which is a solution to the exact equations of motions (i.e. to all orders in perturbation theory, including all higher derivative, quantum and thermal corrections). This configuration mediates the thermal activation of the metastable vacuum to the true ground state, with a decay rate Γ∞ exp(−F_c/T), where F_c is the free energy of the critical bubble. We then compare this exact calculation to various approximations that have been used in previous work. We find that these approximations all overestimate the activation rate. Furthermore, we study the effect of finite baryon number upon the bubble profile and the activation barriers. We find that beyond a critical baryon number the activation barriers disappear altogether.     

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．
     

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.     

Comments on employing the Riesz-Feller derivative in the Schrödinger equation

In this paper, we deal with a fractional Schrödinger equation that contains the quantum Riesz-Feller derivative instead of the Laplace operator in the case of a particle moving in a potential field. In particular, this equation is solved for a free particle in terms of the Fox H-function. On the other hand, we show that from physical viewpoint, the fractional Schrödinger equation with the quantum Riesz-Feller derivative of order α, 0 < α ≤ 2 and skewness θ makes sense only if it reduces to the Laplace operator (α = 2) or to the quantum Riesz fractional derivative (θ = 0). The reason is that the quantum Riesz-Feller derivative is a Hermitian operator and possesses real eigenvalues only when α = 2 or θ = 0. We then focus on the time-independent one-dimensional fractional Schrödinger equation with the quantum Riesz derivative in the case of a particle moving in an infinite potential well. In particular, we show that the explicit formulas for the eigenvalues and eigenfunctions of the time-independent fractional Schrödinger equation that some authors recently claimed to receive cannot be valid. The problem to find right formulas is still open.