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.     

Beating the efficiency of both quantum and classical simulations with a semiclassical method

While rigorous quantum dynamical simulations of many-body systems are extremely difficult (or impossible) due to exponential scaling with dimensionality, the corresponding classical simulations ignore quantum effects. Semiclassical methods are generally more efficient but less accurate than quantum methods and more accurate but less efficient than classical methods. We find a remarkable exception to this rule by showing that a semiclassical method can be both more accurate and faster than a classical simulation. Specifically, we prove that for the semiclassical dephasing representation the number of trajectories needed to simulate quantum fidelity is independent of dimensionality and also that this semiclassical method is even faster than the most efficient corresponding classical algorithm. Analytical results are confirmed with simulations of fidelity in up to 100 dimensions with 2(1700)-dimensional Hilbert space.     

Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system

Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its experimental realization to factor the number 143 on a liquid-crystal NMR quantum processor with dipole-dipole couplings. We believe this to be the largest number factored in quantum-computation realizations, which shows the practical importance of adiabatic quantum algorithms.     

Exponential speedup of quantum newton optimization algorithm for general polynomials

Quantum optimization algorithms can outperform their classical counterpart and are key in modern technology. The second-order optimization algorithm(the Newton algorithm) is a critical optimization method, speeding up the convergence by employing the second-order derivative of loss functions in addition to their first derivative. Here, we propose a new quantum second-order optimization algorithm for general polynomials with a computational complexity of O(poly(log d)). We use this algorithm to solve the nonlinear equation and learning parameter problems in factorization machines. Numerical simulations show that our new algorithm is faster than its classical counterpart and the first-order quantum gradient descent algorithm. While existing quantum Newton optimization algorithms apply only to homogeneous polynomials, our new algorithm can be used in the case of general polynomials, which are more widely present in real applications.     

Demonstration of quantum permutation parity determine algorithm in a superconducting qutrit

A quantum algorithm provides a new way in solving certain computing problems and usually faster than classical algorithms. Here we report an implementation of a quantum algorithm to determine the parity of permutation in a single three-dimensional(3D) superconducting transmon qutrit system. The experiment shows the capacity to speed up in a qutrit,which can also be extended to a multi-level system for solving high-dimensional permutation parity determination problem.     

Quantum Algorithms for Some Well—Known NP Problems

It is known that quantum computer is more powerful than classical computer.In this paper we present quantum algorithms for some famous NP problems in graph theory and combination theory,these quantum algorithms are at least quadratically faster than the classical ones.     

Multimodality Image Fusion Based on Quantum Wavelet Transform and Sum-Modified-Laplacian Rule

The parallelism and entanglement characteristics of quantum computation greatly improve the efficiency of image processing tasks. With the sharp increase of data size and requirement of real-time processing in image fusion application, rapid implementation using quantum computation will become the inexorable trend. A novel multimodality image fusion algorithm based on quantum wavelet transform (QWT) and proposed quantum version of sum-modified-laplacian (SML) rule is designed in this paper. The source digital images are firstly represented by flexible representation of quantum image (FRQI) model, and then the quantum form images are transformed with QWT to capture salient features of source images. The quantum version of SML rule is proposed to fuse wavelet coefficients, which has higher efficiency and runs faster than its classical counterpart. The final fused image is obtained by using inverse quantum wavelet transform. The simulations and theoretical analysis verify that the proposed algorithm is effective in the fusion of multimodality images.

     

Classical random walk with memory versus quantum walk on a one-dimensional infinite chain

Quantum walk is a very useful tool for building quantum algorithms due to the faster spreading of probability distributions as compared to a classical random walk. Comparing the spreading of the probability distributions of a quantum walk with that of a mnemonic classical random walk on a one-dimensional infinite chain, we find that the classical random walk could have a faster spreading than that of the quantum walk conditioned on a finite number of walking steps. Quantum walk surpasses classical random walk with memory in spreading speed when the number of steps is large enough. However, in such a situation, quantum walk would seriously suffer from decoherence. Therefore, classical walk with memory may have some advantages in practical applications.     

A hybrid quantum encoding algorithm of vector quantization for image compression

Many classical encoding algorithms of vector quantization (VQ) of image compression that can obtain global optimal solution have computational complexity O(N). A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45\sqrt{N} times approximately. In this paper, a hybrid quantum VQ encoding algorithm between the classical method and the quantum algorithm is presented. The number of its operations is less than \sqrt{N} for most images, and it is more efficient than the pure quantum algorithm.     

Investigations on quantum correlation of coupled qubits in squeezed vacuum reservoir

In this paper, we investigate the quantum correlation of coupled qubits which are initially in maximally entangled mixed states in squeezed vacuum reservoir. We compare and analyse the effects of squeezed parameters on quantum discord and quantum concurrence. The results show that in squeezed vacuum reservoir, the quantum discord and quantum concurrence perform completely opposite behaviors to the change of squeezed parameters. Quantum discord survives longer with the increase of squeezed amplitude parameter, but entanglement death turns faster on the contrary. The results also indicate that the classical correlation of the system is smaller than quantum discord in vacuum reservoir, while it is bigger than quantum discord in squeezed vacuum reservoir. The quantum discord and classical correlation are more robust than quantum concurrence in the two reservoir environments, which indicates that the entanglement actually is easily affected by decoherence and quantum discord has stronger ability to avoid decoherence in squeezed vacuum reservoir.     

Investigations into quantum correlation of coupled qubits in a squeezed vacuum reservoir

In this paper,we investigate the quantum correlation of coupled qubits which are initially in maximally entangled mixed states in a squeezed vacuum reservoir.We compare and analyze the effects of squeezed parameters on quantum discord and quantum concurrence.The results show that in a squeezed vacuum reservoir,the quantum discord and quantum concurrence perform with completely opposite behaviors with the change of squeezed parameters.Quantum discord survives longer with the increase of squeezed amplitude parameter,but entanglement death is faster on the contrary.The results also indicate that the classical correlation of the system is smaller than quantum discord in a vacuum reservoir,while it is bigger than quantum discord in a squeezed vacuum reservoir.The quantum discord and classical correlation are more robust than quantum concurrence in the two reservoir environments,which indicates that the entanglement actually is easily affected by decoherence and quantum discord has a stronger ability to avoid decoherence in a squeezed vacuum reservoir.     

General approach to quantum-classical hybrid systems and geometric forces

We present a general theoretical framework for a hybrid system that is composed of a quantum subsystem and a classical subsystem. We approach such a system with a simple canonical transformation which is particularly effective when the quantum subsystem is dynamically much faster than the classical counterpart, which is commonly the case in hybrid systems. Moreover, this canonical transformation generates a vector potential which, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics and, on the other hand, yields a Lorentz-like geometric force in the slow classical dynamics.     

A Parallel Quantum Algorithm for the Satisfiability Problem

In this paper we present a classical parallel quantum algorithm for the satisfiability problem. We have exploited the classical parallelism of quantum algorithms developed in [G.L. Long and L. Xiao, Phys. Rev. A 69 （2004） 052303], so that additional acceleration can be gained by using classical parallelism. The quantum algorithm first estimates the number of solutions using the quantum counting algorithm, and then by using the quantum searching algorithm, the explicit solutions are found.     

Preparing a Fast Pauli Decomposition for Variational Quantum Solving Linear Equations

Solving linear equations is a basic and significant mathematical task, and it can be executed by variational quantum algorithm (VQA) with quantum advantages by leveraging near-term quantum device and classical optimizer. In the above algorithm, the coefficient matrix should be decomposed first but slowly with the traditional method, for realizing an effective quantum circuit. In this paper, a general framework for preparing a fast Pauli decomposition for solving arbitrary linear equations using VQA is proposed. This method has a simpler form and reduces the complexity of matrix decomposition compared with the traditional one. Moreover, the concrete tables of two and three qubits cases are given for looking up quickly and the instances of Toeplitz matrix, Yule–Walker, and arbitrary equations are demonstrated. Finally, numerical simulations are given to verify this method. This work provides a more convenient and faster preparatory phase for solving linear equations using VQA.     

A realizable quantum encryption algorithm for qubits

A realizable quantum encryption algorithm for qubits is presented by employing bit-wise quantum computation. System extension and bit-swapping are introduced into the encryption process, which makes the ciphertext space expanded greatly. The security of the proposed algorithm is analysed in detail and the schematic physical implementation is also provided. It is shown that the algorithm, which can prevent quantum attack strategy as well as classical attack strategy, is effective to protect qubits. Finally, we extend our algorithm to encrypt classical binary bits and quantum entanglements.     

Novel qubit block encryption algorithm with hybrid keys

By combining quantum key with classical one, a novel block cryptographic algorithm that can be applied to encrypt qubits is presented. The security of the algorithm is analyzed from several aspects. It is shown that the qubit block encryption algorithm can prevent quantum attacking strategy as well as classical attacking strategy. The hybrid keys are securely reusable after a checking process, which lessens the task of key management significantly. The proposed algorithm offers an alternative to the standard one-time-pad encryption of a quantum bit string using a quantum key.     

A novel quantum block encryption algorithm based on quantum computation

Based on quantum computation, a novel quantum block cryptographic algorithm that can be used to encrypt classical messages is proposed. The security of this algorithm is analyzed from several aspects. It is shown that the quantum block cryptographic algorithm, in which the key can be reused after undergoing a check procedure, can prevent quantum attack strategy as well as classical attack strategy. The problem of key management is discussed and the circuits for encryption and decryption are suggested.     

Size dependence of the minimum excitation gap in the quantum adiabatic algorithm

We study the typical (median) value of the minimum gap in the quantum version of the exact cover problem using quantum Monte Carlo simulations, in order to understand the complexity of the quantum adiabatic algorithm for much larger sizes than before. For a range of sizes N< or =128, where the classical Davis-Putnam algorithm shows exponential median complexity, the quantum adiabatic algorithm shows polynomial median complexity. The bottleneck of the algorithm is an isolated avoided-crossing point of a Landau-Zener type (collision between the two lowest energy levels only).     

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。     

Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations

A novel encryption algorithm for quantum images based on quantum image XOR operations is designed. The quantum image XOR operations are designed by using the hyper-chaotic sequences generated with the Chen’s hyper-chaotic system to control the control-NOT operation, which is used to encode gray-level information. The initial conditions of the Chen’s hyper-chaotic system are the keys, which guarantee the security of the proposed quantum image encryption algorithm. Numerical simulations and theoretical analyses demonstrate that the proposed quantum image encryption algorithm has larger key space, higher key sensitivity, stronger resistance of statistical analysis and lower computational complexity than its classical counterparts.