Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems

Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex.Here,we propose a variational quantum algorithm for solving the non-Hermitian Hamiltonian by minimizing a type of energy variance,where zero variance can naturally determine the eigenvalues and the associated left and right eigenstates.Moreover,the energy is set as a parameter in the cost function and can be tuned to scan the whole spectrum efficiently by using a two-step optimization scheme.Through numerical simulations,we demonstrate the algorithm for preparing the left and right eigenstates,verifying the biorthogonal relations,as well as evaluating the observables.We also investigate the impact of quantum noise on our algorithm and show that its performance can be largely improved using error mitigation techniques.Therefore,our work suggests an avenue for solving non-Hermitian quantum many-body systems with variational quantum algorithms on near-term noisy quantum computers.

Quantum algorithm for minimum dominating set problem with circuit design

Using quantum algorithms to solve various problems has attracted widespread attention with the development of quantum computing.Researchers are particularly interested in using the acceleration properties of quantum algorithms to solve NP-complete problems.This paper focuses on the well-known NP-complete problem of finding the minimum dominating set in undirected graphs.To expedite the search process,a quantum algorithm employing Grover’s search is proposed.However,a challenge arises from the unknown number of solutions for the minimum dominating set,rendering direct usage of original Grover’s search impossible.Thus,a swap test method is introduced to ascertain the number of iterations required.The oracle,diffusion operators,and swap test are designed with achievable quantum gates.The query complexity is O(1.414^(n))and the space complexity is O(n).To validate the proposed approach,qiskit software package is employed to simulate the quantum circuit,yielding the anticipated results.

Development of a Post Quantum Encryption Key Generation Algorithm Using Electromagnetic Wave Propagation Theory

In today’s rapid widespread of digital technologies into all live aspects to enhance efficiency and productivity on the one hand and on the other hand ensure customer engagement, personal data counterfeiting has become a major concern for businesses and end-users. One solution to ensure data security is encryption, where keys are central. There is therefore a need to find robusts key generation implementation that is effective, inexpensive and non-invasive for protecting and preventing data counterfeiting. In this paper, we use the theory of electromagnetic wave propagation to generate encryption keys.

Memory-Occupied Routing Algorithms for Quantum Relay Networks

Quantum transmission experiments have shown that the success-ful transmission rate of entangled quanta in optical fibers decreases expo-nentially.Although current quantum networks deploy quantum relays to establish long-distance connections,the increase in transmission distance and entanglement switching costs still need to be considered when selecting the next hop.However,most of the existing quantum network models prefer to consider the parameters of the physical layer,which ignore the influence factors of the network layer.In this paper,we propose a meshy quantum network model based on quantum teleportation,which considers both net-work layer and physical layer parameters.The proposed model can reflect the realistic transmission characteristics and morphological characteristics of the quantum relay network.Then,we study the network throughput of different routing algorithms with the same given parameters when multiple source-destination pairs are interconnected simultaneously.To solve the chal-lenges of routing competition caused by the simultaneous transmission,we present greedy memory-occupied algorithm Q-GMOA and random memory-occupied algorithm Q-RMOA.The proposed meshy quantum network model and the memory-occupied routing algorithms can improve the utilization rate of resources and the transmission performance of the quantum network.And the evaluation results indicate that the proposed methods embrace a higher transmission rate than the previous methods with repeater occupation.

Comparison of differential evolution, particle swarm optimization,quantum-behaved particle swarm optimization, and quantum evolutionary algorithm for preparation of quantum states

Four intelligent optimization algorithms are compared by searching for control pulses to achieve the preparation of target quantum states for closed and open quantum systems, which include differential evolution(DE), particle swarm optimization(PSO), quantum-behaved particle swarm optimization(QPSO), and quantum evolutionary algorithm(QEA).We compare their control performance and point out their differences. By sampling and learning for uncertain quantum systems, the robustness of control pulses found by these four algorithms is also demonstrated and compared. The resulting research shows that the QPSO nearly outperforms the other three algorithms for all the performance criteria considered.This conclusion provides an important reference for solving complex quantum control problems by optimization algorithms and makes the QPSO be a powerful optimization tool.

A quantum algorithm for Toeplitz matrix-vector multiplication

Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quantum algorithm for Toeplitz matrix-vector multiplication with time complexity O(κpolylogn),whereκand 2n are the condition number and the dimension of the circulant matrix extended from the Toeplitz matrix,respectively.For the case with an unknown generating function,we also give a corresponding non-asymptotic quantum version that eliminates the dependency on the L_(1)-normρof the displacement of the structured matrices.Due to the good use of the special properties of Toeplitz matrices,the proposed quantum algorithms are sufficiently accurate and efficient compared to the existing quantum algorithms under certain circumstances.

Technique for Multi-Pass Turning Optimization Based on Gaussian Quantum-Behaved Bat Algorithm

The multi-pass turning operation is one of the most commonly used machining methods in manufacturing field.The main objective of this operation is to minimize the unit production cost.This paper proposes a Gaussian quantum-behaved bat algorithm(GQBA)to solve the problem of multi-pass turning operation.The proposed algorithm mainly includes the following two improvements.The first improvement is to incorporate the current optimal positions of quantum bats and the global best position into the stochastic attractor to facilitate population diversification.The second improvement is to use a Gaussian distribution instead of the uniform distribution to update the positions of the quantum-behaved bats,thus performing a more accurate search and avoiding premature convergence.The performance of the presented GQBA is demonstrated through numerical benchmark functions and amulti-pass turning operation problem.Thirteen classical benchmark functions are utilized in the comparison experiments,and the experimental results for accuracy and convergence speed demonstrate that,in most cases,the GQBA can provide a better search capability than other algorithms.Furthermore,GQBA is applied to an optimization problem formulti-pass turning,which is designed tominimize the production cost while considering many practical machining constraints in the machining process.The experimental results indicate that the GQBA outperforms other comparison algorithms in terms of cost reduction,which proves the effectiveness of the GQBA.

Quantum Algorithm for Mining Frequent Patterns for Association Rule Mining

Maximum frequent pattern generation from a large database of transactions and items for association rule mining is an important research topic in data mining. Association rule mining aims to discover interesting correlations, frequent patterns, associations, or causal structures between items hidden in a large database. By exploiting quantum computing, we propose an efficient quantum search algorithm design to discover the maximum frequent patterns. We modified Grover’s search algorithm so that a subspace of arbitrary symmetric states is used instead of the whole search space. We presented a novel quantum oracle design that employs a quantum counter to count the maximum frequent items and a quantum comparator to check with a minimum support threshold. The proposed derived algorithm increases the rate of the correct solutions since the search is only in a subspace. Furthermore, our algorithm significantly scales and optimizes the required number of qubits in design, which directly reflected positively on the performance. Our proposed design can accommodate more transactions and items and still have a good performance with a small number of qubits.

Quantum control based on three forms of Lyapunov functions

This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.

An anti-aliasing filtering of quantum images in spatial domain using a pyramid structure

As a part of quantum image processing,quantum image filtering is a crucial technology in the development of quantum computing.Low-pass filtering can effectively achieve anti-aliasing effects on images.Currently,most quantum image filterings are based on classical domains and grayscale images,and there are relatively fewer studies on anti-aliasing in the quantum domain.This paper proposes a scheme for anti-aliasing filtering based on quantum grayscale and color image scaling in the spatial domain.It achieves the effect of anti-aliasing filtering on quantum images during the scaling process.First,we use the novel enhanced quantum representation(NEQR)and the improved quantum representation of color images(INCQI)to represent classical images.Since aliasing phenomena are more pronounced when images are scaled down,this paper focuses only on the anti-aliasing effects in the case of reduction.Subsequently,we perform anti-aliasing filtering on the quantum representation of the original image and then use bilinear interpolation to scale down the image,achieving the anti-aliasing effect.The constructed pyramid model is then used to select an appropriate image for upscaling to the original image size.Finally,the complexity of the circuit is analyzed.Compared to the images experiencing aliasing effects solely due to scaling,applying anti-aliasing filtering to the images results in smoother and clearer outputs.Additionally,the anti-aliasing filtering allows for manual intervention to select the desired level of image smoothness.

Simulation of optimal work extraction for quantum systems with work storage

The capacity to extract work from a quantum heat machine is not only of practical value but also lies at the heart of understanding quantum thermodynamics.In this paper,we investigate optimal work extraction for quantum systems with work storage,where extracting work is completed by a unitary evolution on the composite system.We consider the physical requirement of energy conservation both strictly and on average.For both,we construct their corresponding unitaries and propose variational quantum algorithms for optimal work extraction.We show that maximal work extraction in general can be feasible when energy conservation is satisfied on average.We demonstrate with numeral simulations using a continuous-variable work storage.Our work show an implementation of a variational quantum computing approach for simulating work extraction in quantum systems.

Effects of T-Factor on Quantum Annealing Algorithms for Integer Factoring Problem

The hardness of the integer factoring problem(IFP)plays a core role in the security of RSA-like cryptosystems that are widely used today.Besides Shor’s quantum algorithm that can solve IFP within polynomial time,quantum annealing algorithms(QAA)also manifest certain advantages in factoring integers.In experimental aspects,the reported integers that were successfully factored by using the D-wave QAA platform are much larger than those being factored by using Shor-like quantum algorithms.In this paper,we report some interesting observations about the effects of QAA for solving IFP.More specifically,we introduce a metric,called T-factor that measures the density of occupied qubits to some extent when conducting IFP tasks by using D-wave.We find that T-factor has obvious effects on annealing times for IFP:The larger of T-factor,the quicker of annealing speed.The explanation of this phenomenon is also given.

A new quantum key distribution resource allocation and routing optimization scheme

Quantum key distribution(QKD)is a technology that can resist the threat of quantum computers to existing conventional cryptographic protocols.However,due to the stringent requirements of the quantum key generation environment,the generated quantum keys are considered valuable,and the slow key generation rate conflicts with the high-speed data transmission in traditional optical networks.In this paper,for the QKD network with a trusted relay,which is mainly based on point-to-point quantum keys and has complex changes in network resources,we aim to allocate resources reasonably for data packet distribution.Firstly,we formulate a linear programming constraint model for the key resource allocation(KRA)problem based on the time-slot scheduling.Secondly,we propose a new scheduling scheme based on the graded key security requirements(GKSR)and a new micro-log key storage algorithm for effective storage and management of key resources.Finally,we propose a key resource consumption(KRC)routing optimization algorithm to properly allocate time slots,routes,and key resources.Simulation results show that the proposed scheme significantly improves the key distribution success rate and key resource utilization rate,among others.

O(logN) Algorithm for Amplitude Amplification and O(logN) Algorithms for Amplitude Transfer in Grover’s Algorithm

Grovers algorithm is a category of quantum algorithms that can be applied to many problems through the exploitation of quantum parallelism. The Amplitude Amplification in Grovers algorithm is T = O(N). This paper introduces two new algorithms for Amplitude Amplification in Grovers algorithm with a time complexity of T = O(logN), aiming to improve efficiency in quantum computing. The difference between Grovers algorithm and our first algorithm is that the Amplitude Amplification ratio in Grovers algorithm is an arithmetic series and ours, a geometric one. Because our Amplitude Amplification ratios converge much faster, the time complexity is improved significantly. In our second algorithm, we introduced a new concept, Amplitude Transfer where the marked state is transferred to a new set of qubits such that the new qubit state is an eigenstate of measurable variables. When the new qubit quantum state is measured, with high probability, the correct solution will be obtained.

Time Complexity of the Oracle Phase in Grover’s Algorithm

Since Grover’s algorithm was first introduced, it has become a category of quantum algorithms that can be applied to many problems through the exploitation of quantum parallelism. The original application was the unstructured search problems with the time complexity of O(). In Grover’s algorithm, the key is Oracle and Amplitude Amplification. In this paper, our purpose is to show through examples that, in general, the time complexity of the Oracle Phase is O(N), not O(1). As a result, the time complexity of Grover’s algorithm is O(N), not O(). As a secondary purpose, we also attempt to restore the time complexity of Grover’s algorithm to its original form, O(), by introducing an O(1) parallel algorithm for unstructured search without repeated items, which will work for most cases. In the worst-case scenarios where the number of repeated items is O(N), the time complexity of the Oracle Phase is still O(N) even after additional preprocessing.

Multipath Selection Algorithm Based on Dynamic Flow Prediction

Traditional traffic management techniques appear to be incompetent in complex data center networks, so proposes a load balancing strategy based on Long Short-Term Memory (LSTM) and quantum annealing by Software Defined Network (SDN) to dynamically predict the traffic and comprehensively consider the current and predicted load of the network in order to select the optimal forwarding path and balance the network load. Experiments have demonstrated that the algorithm achieves significant improvement in both system throughput and average packet loss rate for the purpose of improving network quality of service.

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.

Improved quantum bacterial foraging algorithm for tuning parameters of fractional-order PID controller

The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is discrete and constant,which cannot affect the situation of the solution space and limit the diversity of bacterial population. In this paper, an improved QBFO(IQBFO) algorithm is proposed, which can adaptively make the quantum rotation angle continuously updated and enhance the global search ability. In the initialization process, the modified probability of the optimal rotation angle is introduced to avoid the existence of invariant solutions. The modified operator of probability amplitude is adopted to further increase the population diversity.The tests based on benchmark functions verify the effectiveness of the proposed algorithm. Moreover, compared with the integerorder PID controller, the fractional-order proportion integration differentiation(PID) controller increases the complexity of the system with better flexibility and robustness. Thus the fractional-order PID controller is applied to the servo system. The tuning results of PID parameters of the fractional-order servo system show that the proposed algorithm has a good performance in tuning the PID parameters of the fractional-order servo system.

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√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 √N for most images, and it is more efficient than the pure quantum algorithm.

Enhanced minimum attribute reduction based on quantum-inspired shuffled frog leaping algorithm

Attribute reduction in the rough set theory is an important feature selection method, but finding a minimum attribute reduction has been proven to be a non-deterministic polynomial （NP）-hard problem. Therefore, it is necessary to investigate some fast and effective approximate algorithms. A novel and enhanced quantum-inspired shuffled frog leaping based minimum attribute reduction algorithm （QSFLAR） is proposed. Evolutionary frogs are represented by multi-state quantum bits, and both quantum rotation gate and quantum mutation operators are used to exploit the mechanisms of frog population diversity and convergence to the global optimum. The decomposed attribute subsets are co-evolved by the elitist frogs with a quantum-inspired shuffled frog leaping algorithm. The experimental results validate the better feasibility and effectiveness of QSFLAR, comparing with some representa- tive algorithms. Therefore, QSFLAR can be considered as a more competitive algorithm on the efficiency and accuracy for minimum attribute reduction.