Simulated quantum computation of global minima

Finding the optimal solution to a complex optimisation problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The number of function evaluations N reduced from O(N) in classical simulation to O(N ^1/2) in quantum simulation. We also show how the Grover's quantum algorithm can be combined with the classical Pivot method for global optimisation to treat larger systems.     

Compressed quantum simulation of the Ising model

Jozsa et al. [Proc. R. Soc. A 466, 809 2009)] have shown that a match gate circuit running on n qubits can be compressed to a universal quantum computation on log(n)+3 qubits. Here, we show how this compression can be employed to simulate the Ising interaction of a 1D chain consisting of n qubits using a universal quantum computer running on log(n) qubits. We demonstrate how the adiabatic evolution can be realized on this exponentially smaller system and how the magnetization, which displays a quantum phase transition, can be measured. This shows that the quantum phase transition of very large systems can be observed experimentally with current technology.     

Experimental implementation of an adiabatic quantum optimization algorithm

We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to solve hard problems. This experiment uses a particularly well-suited three quantum bit molecule and was made possible by introducing a technique that encodes general instances of the given optimization problem into an easily applicable Hamiltonian. Our results indicate an optimal run time of the adiabatic algorithm that agrees well with the prediction of a simple decoherence model.     

Factoring larger integers with fewer qubits via quantum annealing with optimized parameters

RSA cryptography is based on the difficulty of factoring large integers, which is an NP-hard(and hence intractable) problem for a classical computer. However, Shor's algorithm shows that its complexity is polynomial for a quantum computer, although technical difficulties mean that practical quantum computers that can tackle integer factorizations of meaningful size are still a long way away. Recently, Jiang et al. proposed a transformation that maps the integer factorization problem onto the quadratic unconstrained binary optimization(QUBO) model. They tested their algorithm on a D-Wave 2000 Q quantum annealing machine, raising the record for a quantum factorized integer to 376289 with only 94 qubits. In this study, we optimize the problem Hamiltonian to reduce the number of qubits involved in the final Hamiltonian while maintaining the QUBO coefficients in a reasonable range, enabling the improved algorithm to factorize larger integers with fewer qubits. Tests of our improved algorithm using D-Wave's hybrid quantum/classical simulator qbsolv confirmed that performance was improved, and we were able to factorize 1005973, a new record for quantum factorized integers, with only 89 qubits. In addition, our improved algorithm can tolerate more errors than the original one. Factoring 1005973 using Shor's algorithm would require about 41 universal qubits,which current universal quantum computers cannot reach with acceptable accuracy. In theory, the latest IBM Q System OneTM(Jan. 2019) can only factor up to 10-bit integers, while the D-Wave have a thousand-fold advantage on the factoring scale. This shows that quantum annealing machines, such as those by D-Wave, may be close to cracking practical RSA codes, while universal quantum-circuit-based computers may be many years away from attacking RSA.     

Remote interactions between two d-dimensional distributed quantum systems： nonlocal generalized quantum control-NOT gate and entanglement swapping

We present a systematic simple method to implement a generalized quantum control-NOT （CNOT） gate on two d-dimensional distributed systems. First, we show how the nonlocal generalized quantum CNOT gate can be implemented with unity fidelity and unity probability by using a maximally entangled pair of qudits as a quantum channel. We also put forward a scheme for probabilistically implementing the nonlocal operation with unity fidelity by employing a partially entangled qudit pair as a quantum channel. Analysis of the scheme indicates that the use of partially entangled quantum channel for implementing the nonlocal generalized quantum CNOT gate leads to the problem of ＇the general optimal information extraction＇. We also point out that the nonlocal generalized quantum CNOT gate can be used in the entanglement swapping between particles belonging to distant users in a communication network and distributed quantum computer.[第一段]     

Rashba control to minimize circuit cost of quantum Fourier algorithm in ballistic nanowires

The presented work provides a new prospective of quantum computer hardware development through ballistic nanowires with Rashba effect. We address Rashba effect as a possible mechanism to realize novel qubit gates in nanowires. We apply our results to the design of a new quantum circuit for Fourier algorithm, which shows an improved quantum cost in terms of the number of gates. The current system can be successfully implemented to increase the production of quantum computer experimentally thanks to the absence of impurities. The introduced circuit will enhance the scope of experimental and theoretical research for the realization of other quantum algorithms, such as phase estimation and Shor's algorithms.     

Scheme for Implementing Refined Deutsch-Jozsa Algorithm via Superconducing Qubits

We propose a scheme of implementing the Deutsch-Jozsa algorithm based on superconducing charge qubits, which would be a key step to scale more complex quantum algorithms and very important for constructing a real quantum computer via superconducting charge qubits. The present scheme is simple but fairly efficient, and easily manipulated because arbitrary two-qubit can be selectively and effectively coupled by a common inductance. More manipulations can be carried out before decoherence sets in. The proposed scheme is in line with current technology.     

Stable quantum computation of unstable classical chaos

We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with moderate imperfections is able to simulate accurately the unstable chaotic classical nonlinear dynamics for long times. The algorithm can be easily implemented on systems of a few qubits.     

Development of High Performance Quantum Image Algorithm on Constrained Least Squares Filtering Computation

Recent development of computer technology may lead to the quantum image algorithms becoming a hotspot. Quantum information and computation give some advantages to our quantum image algorithms, which deal with the limited problems that cannot be solved by the original classical image algorithm. Image processing cry out for applications of quantum image. Most works on quantum images are theoretical or sometimes even unpolished, although real-world experiments in quantum computer have begun and are multiplying. However, just as the development of computer technology helped to drive the Technology Revolution, a new quantum image algorithm on constrained least squares filtering computation was proposed from quantum mechanics, quantum information, and extremely powerful computer. A quantum image representation model is introduced to construct an image model, which is then used for image processing. Prior knowledge is employed in order to reconstruct or estimate the point spread function, and a non-degenerate estimate is obtained based on the opposite processing. The fuzzy function against noises is solved using the optimal measure of smoothness. On the constraint condition, determine the minimum criterion function and estimate the original image function. For some motion blurs and some kinds of noise pollutions, such as Gaussian noises, the proposed algorithm is able to yield better recovery results. Additionally, it should be noted that, when there is a noise attack with very low noise intensity, the model based on the constrained least squares filtering can still deliver good recovery results, with strong robustness. Subsequently, discuss the simulation analysis of the complexity of implementing quantum circuits and image filtering, and demonstrate that the algorithm has a good effect on fuzzy recovery, when the noise density is small.     

Feature Selection for Recommender Systems with Quantum Computing

The promise of quantum computing to open new unexplored possibilities in several scientific fields has been long discussed, but until recently the lack of a functional quantum computer has confined this discussion mostly to theoretical algorithmic papers. It was only in the last few years that small but functional quantum computers have become available to the broader research community. One paradigm in particular, quantum annealing, can be used to sample optimal solutions for a number of NP-hard optimization problems represented with classical operations research tools, providing an easy access to the potential of this emerging technology. One of the tasks that most naturally fits in this mathematical formulation is feature selection. In this paper, we investigate how to design a hybrid feature selection algorithm for recommender systems that leverages the domain knowledge and behavior hidden in the user interactions data. We represent the feature selection as an optimization problem and solve it on a real quantum computer, provided by D-Wave. The results indicate that the proposed approach is effective in selecting a limited set of important features and that quantum computers are becoming powerful enough to enter the wider realm of applied science.     

Exponential gain in quantum computing of quantum chaos and localization

We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization, and Anderson transition can be modeled efficiently on a quantum computer. We also show that a similar algorithm simulates efficiently classical chaos in certain area-preserving maps.     

Quantum computing methods for electronic states of the water molecule

ABSTRACT

We compare recently proposed methods to compute the electronic state energies of the water molecule on a quantum computer. The methods include the phase estimation algorithm based on Trotter decomposition, the phase estimation algorithm based on the direct implementation of the Hamiltonian, direct measurement based on the implementation of the Hamiltonian and a specific variational quantum eigensolver, Pairwise VQE. After deriving the Hamiltonian using STO-3G basis, we first explain how each method works and then compare the simulation results in terms of gate complexity and the number of measurements for the ground state of the water molecule with different O–H bond lengths. Moreover, we present the analytical analyses of the error and the gate-complexity for each method. While the required number of qubits for each method is almost the same, the number of gates and the error vary a lot. In conclusion, among methods based on the phase estimation algorithm, the second-order direct method provides the most efficient circuit implementations in terms of the gate complexity. Moreover, Pairwise VQE serves the most practical method for near-term applications on the current available quantum computers. Finally the possibility of extending the calculation to excited states and resonances is discussed.     

Mesoscopic one-way channels for quantum state transfer via the quantum Hall effect

We show that the one-way channel formalism of quantum optics has a physical realization in electronic systems. In particular, we show that magnetic edge states form unidirectional quantum channels capable of coherently transporting electronic quantum information. Using the equivalence between one-way photonic channels and magnetic edge states, we adapt a proposal for quantum state transfer to mesoscopic systems using edge states as a quantum channel, and show that it is feasible with reasonable experimental parameters. We discuss how this protocol may be used to transfer information encoded in number, charge, or spin states of quantum dots, so it may prove useful for transferring quantum information between parts of a solid-state quantum computer.     

量子算法的NMR实现方法

量子计算机是一种以量子耦合方式进行信息处理的装置[1 ] 。原则上 ,它能利用量子相干干涉方法以比传统计算机更快的速度进行诸如大数的因式分解、未排序数据库中的数据搜索等工作[2 ] 。建造大型量子计算机的主要困难是噪音、去耦和制造工艺。一方面 ,虽然离子陷阱和光学腔实验方法大有希望 ,但这些方法都还没有成功实现过量子计算。另一方面 ,因为隔离于自然环境 ,核自旋可以成为很好的“量子比特” ,可能以非传统方式使用核磁共振 (NMR)技术实现量子计算。本文介绍一种用NMR方法实现量子计算的方法 ,该方法能够用比传统方法少的步骤解决一个纯数学问题。基于该方法的简单量子计算机使用比传统计算机使用更少的函数“调用”判断一未知函数的类别。     

Efficient classical simulation of continuous variable quantum information processes

We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators (including finite losses) and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.     

Ramsey numbers and adiabatic quantum computing

The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.     

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...     

混合态数据库的Grover算法数学形式及其搜索成功率

Grover提出了容量为N的数据库量子搜索法.只需进行O(平方根N)次迭代就能以几乎为1的概率实现对目标的搜索.本文将文献[1]的Grover搜索法推广到混合态情形,给出了一个基于混合态的Grover搜索法,并分析了该搜索法成功的概率上界.进一步发现搜索法成功的概率完全依赖于所使用的初态(混合态).该结论为了解量子噪声对Grover搜索法的影响提供一定的理论依据.最后通过例子说明了如何实施基于混合态的Grover搜索法.     

Manipulating atoms and molecules with evanescent-wave mirrors

We explore how atoms and polar molecules can be manipulated using evanescent-wave mirrors (EWM). We review the simpler case of ultracold atoms incident on EWM, and show that quantum effects such as tunneling, above barrier reflection, and Casimir retardation corrections, can be probed. We show that it is possible to enhance significantly quantum effects by engineering sharp features in the effective atom-EWM potential. We illustrate the concept with a bichromatic EWM created by using red and blue detuned lasers. Finally, we extend the treatment to ultracold diatomic polar molecules. Quantum reflection and molecular state selection are demonstrated under attainable physical conditions. By facilitating the manipulation and trapping of ultracold molecules, such molecular mirrors could have several applications, e.g., as devices to filter and select state for ultracold chemistry, or to manipulate states for quantum information processing.     

Nonlocally correlated trajectories in two-particle quantum mechanics

In this paper we present a series of computer calculations carried out in order to demonstrate exactly how the de Broglie-Bohm interpretation works for two-particle quantum mechanics. In particular, we show how the de Broglie-Bohm interpretation can account for the essential features of nonrelativistic, two-particle quantum mechanics in terms of well-defined, correlated, individual particle trajectories and spin vectors. We demonstrate exactly how both quantum statistics and the correlations observed in Einstein-Podolsky-Rosen experiments can be explained in terms of nonlocal quantum potentials and nonlocal quantum torques which act on the well-defined individual particle coordinates and spin vectors.