On the time-independent Hamiltonian in real-time and imaginary-time quantum annealing

We present the analog analogue of Grover's problem as an example of the time-independent Hamiltonian for applying the speed limit of the imaginary-time Schrödinger equation derived by Okuyama and Ohzeki and the new class of energy-time uncertainty relation proposed by Kieu. It is found that the computational time of the imaginary-time quantum annealing of this Grover search can be exponentially small, while the counterpart of the quantum evolution driven by the real-time Schrödinger equation could only provide square root speedup, compared with classic search. The present results are consistent with the cases of the time-dependent quantum evolution of the natural Grover problem in previous works. We once again emphasize that the logarithm and square root algorithmic performances are generic in imaginary-time quantum annealing and quantum evolution driven by real-time Schrödinger equation, respectively. Also, we provide evidences to search deep reasons why the imaginary-time quantum annealing can lead to exponential speedup and the real-time quantum annealing can make square root speedup.

Quantum annealing for semi-supervised learning

Recent advances in quantum technology have led to the development and the manufacturing of programmable quantum annealers that promise to solve certain combinatorial optimization problems faster than their classical counterparts.Semi-supervised learning is a machine learning technique that makes use of both labeled and unlabeled data for training,which enables a good classifier with only a small amount of labeled data.In this paper,we propose and theoretically analyze a graph-based semi-supervised learning method with the aid of the quantum annealing technique,which efficiently utilizes the quantum resources while maintaining good accuracy.We illustrate two classification examples,suggesting the feasibility of this method even with a small portion(30%) of labeled data involved.

A New Path to Create Solutions for Quantum Annealing Problems

Quantum computing has already become a technology to be used by large companies in finance, distribution, health care, chemistry, etc. Among the different approaches, quantum annealing is one of the most promising in the short term. However, software development platforms do not offer user-friendly interfaces for the definition of annealing problems. In this paper we present a solution to this problem: QPath®’s Annealer Compositor that facilitates the definition and execution of annealing algorithms in either quantum annealing or digital annealing computers. An example based on a nurse work schedule is used for illustrating this special interface.

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.

Traffic Clustering Algorithm of Urban Data Brain Based on a Hybrid-Augmented Architecture of Quantum Annealing and Brain-Inspired Cognitive Computing

In recent years,the urbanization process has brought modernity while also causing key issues,such as traffic congestion and parking conflicts.Therefore,cities need a more intelligent"brain"to form more intelligent and efficient transportation systems.At present,as a type of machine learning,the traditional clustering algorithm still has limitations.K-means algorithm is widely used to solve traffic clustering problems,but it has limitations,such as sensitivity to initial points and poor robustness.Therefore,based on the hybrid architecture of Quantum Annealing(QA)and brain-inspired cognitive computing,this study proposes QA and Brain-Inspired Clustering Algorithm(QABICA)to solve the problem of urban taxi-stand locations.Based on the traffic trajectory data of Xi’an and Chengdu provided by Didi Chuxing,the clustering results of our algorithm and K-means algorithm are compared.We find that the average taxi-stand location bias of the final result based on QABICA is smaller than that based on K-means,and the bias of our algorithm can effectively reduce the tradition K-means bias by approximately 42%,up to approximately 83%,with higher robustness.QA algorithm is able to jump out of the local suboptimal solutions and approach the global optimum,and brain-inspired cognitive computing provides search feedback and direction.Thus,we will further consider applying our algorithm to analyze urban traffic flow,and solve traffic congestion and other key problems in intelligent transportation.

Numerical Computation of a Mixed-Integer Optimal Control Problem Based on Quantum Annealing

It is extremely challenging to solve the mixed-integer optimal control problems(MIOCPs)due to the complex computation in solving the integer decision variables.This paper presents a new method based on quantum annealing(QA)to solve MIOCP.The QA is a metaheuristic which applies quantum tunneling in the annealing process.It has a faster convergence speed in optimal-searching and is less likely to run into local minima.Hence,QA is applied to deal with this kind of optimization problems.First,MIOCP is transformed into a mixed-integer nonlinear programming(MINLP).Then,a method based on QA is adopted to solve the MINLP and acquire the optimal solution.At last,two benchmark examples including Lotka-Volterra type fishing problem and distillation column are presented and solved.The effectiveness of the metliodology is verified by the acquired optimal schemes.

Quantum Computational Techniques for Prediction of Cognitive State of Human Mind from EEG Signals

The utilization of quantum states for the representation of information and the advances in machine learning is considered as an efficient way of modeling the working of complex systems.The states of mind or judgment outcomes are highly complex phenomena that happen inside the human body.Decoding these states is significant for improving the quality of technology and providing an impetus to scientific research aimed at understanding the functioning of the human mind.One of the key advantages of quantum wave-functions over conventional classical models is the existence of configurable hidden variables,which provide more data density due to its exponential state-space growth.These hidden variables correspond to the amplitudes of each probable state of the system and allow for the modeling of various intricate aspects of measurable and observable physical quantities.This makes the quantum wave-functions powerful and felicitous to model cognitive states of the human mind,as it inherits the ability to efficiently couple the current context with past experiences temporally and spatially to approach an appropriate future cognitive state.This paper implements and compares some techniques like Variational Quantum Classifiers(VQC),quantum annealing classifiers,and hybrid quantum-classical neural networks,to harness the power of quantum computing for processing cognitive states of the mind by making use of EEG data.It also introduces a novel pipeline by logically combining some of the aforementioned techniques,to predict future cognitive responses.The preliminary results of these approaches are presented and are very encouraging with upto 61.53%validation accuracy.

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.

Prestack seismic stochastic inversion based on statistical characteristic parameters

In the conventional stochastic inversion method,the spatial structure information of underground strata is usually characterized by variograms.However,effectively characterizing the heterogeneity of complex strata is difficult.In this paper,multiple parameters are used to fully explore the underground formation information in the known seismic reflection and well log data.The spatial structure characteristics of complex underground reservoirs are described more comprehensively using multiple statistical characteristic parameters.We propose a prestack seismic stochastic inversion method based on prior information on statistical characteristic parameters.According to the random medium theory,this method obtains several statistical characteristic parameters from known seismic and logging data,constructs a prior information model that meets the spatial structure characteristics of the underground strata,and integrates multiparameter constraints into the likelihood function to construct the objective function.The very fast quantum annealing algorithm is used to optimize and update the objective function to obtain the fi nal inversion result.The model test shows that compared with the traditional prior information model construction method,the prior information model based on multiple parameters in this paper contains more detailed stratigraphic information,which can better describe complex underground reservoirs.A real data analysis shows that the stochastic inversion method proposed in this paper can effectively predict the geophysical characteristics of complex underground reservoirs and has a high resolution.

New Advanced Computing Architecture for Cryptography Design and Analysis by D-Wave Quantum Annealer

Universal quantum computers are far from achieving practical applications.The D-Wave quantum computer is initially designed for combinatorial optimizations.Therefore,exploring the potential applications of the D-Wave device in the field of cryptography is of great importance.First,although we optimize the general quantum Hamiltonian on the basis of the structure of the multiplication table(factor up to 1005973),this study attempts to explore the simplification of Hamiltonian derived from the binary structure of the integers to be factored.A simple factorization on 143 with four qubits is provided to verify the potential of further advancing the integer-factoring ability of the D-Wave device.Second,by using the quantum computing cryptography based on the D-Wave 2000 Q system,this research further constructs a simple version of quantum-classical computing architecture and a Quantum-Inspired Simulated Annealing(QISA)framework.Good functions and a high-performance platform are introduced,and additional balanced Boolean functions with high nonlinearity and optimal algebraic immunity can be found.Further comparison between QISA and Quantum Annealing(QA)on six-variable bent functions not only shows the potential speedup of QA,but also suggests the potential of architecture to be a scalable way of D-Wave annealer toward a practical cryptography design.

Shaping the future of the application of quantum computing in intelligent transportation system

The intelligent transportation system(ITS)integrates a variety of advanced science and technology to support and monitor road traffic systems and accelerate the urbanization process of various countries.This paper analyzes the shortcomings of ITS,introduces the principle of quantum computing and the performance of universal quantum computer and special-purpose quantum computer,and shows how to use quantum advantages to improve the existing ITS.The application of quantum computer in transportation field is reviewed from three application directions:path planning,transportation operation management,and transportation facility layout.Due to the slow development of the current universal quantum computer,the D-Wave quantum machine is used as a breakthrough in the practical application.This paper makes it clear that quantum computing is a powerful tool to promote the development of ITS,emphasizes the importance and necessity of introducing quantum computing into intelligent transportation,and discusses the possible development direction in the future.

A Quantum Computing Based Numerical Method for Solving Mixed-Integer Optimal Control Problems

Mixed-integer optimal control problems(MIOCPs) usually play important roles in many real-world engineering applications. However, the MIOCP is a typical NP-hard problem with considerable computational complexity, resulting in slow convergence or premature convergence by most current heuristic optimization algorithms. Accordingly, this study proposes a new and effective hybrid algorithm based on quantum computing theory to solve the MIOCP. The algorithm consists of two parts:(i) Quantum Annealing(QA) specializes in solving integer optimization with high efficiency owing to the unique annealing process based on quantum tunneling, and(ii) Double-Elite Quantum Ant Colony Algorithm(DEQACA) which adopts double-elite coevolutionary mechanism to enhance global searching is developed for the optimization of continuous decisions. The hybrid QA/DEQACA algorithm integrates the strengths of such algorithms to better balance the exploration and exploitation abilities. The overall evolution performs to seek out the optimal mixed-integer decisions by interactive parallel computing of the QA and the DEQACA. Simulation results on benchmark functions and practical engineering optimization problems verify that the proposed numerical method is more excel at achieving promising results than other two state-of-the-art heuristics.

Deciphering a Million-Plus RSA Integer with Ultralow Local Field Coefficient h and Coupling Coefficient J of the Ising Model by D-Wave 2000Q

This work is the first to determine that a real quantum computer(including generalized and specialized)can decipher million-scale RSA relying solely on quantum algorithms,showing the real attack potential of D-Wave machines.The influence of different column widths on RSA factorization results is studied on the basis of a multiplication table,and the optimal column method is determined by traversal experiments.The traversal experiment of integer factorization within 10000 shows that the local field and coupling coefficients are 75%–93%lower than the research of Shanghai University in 2020 and more than 85%lower than that of Purdue University in 2018.Extremely low Ising model parameters are crucial to reducing the hardware requirements,prompting factoring 1245407 on the D-Wave 2000Q real machine.D-Wave advantage already has more than 5000 qubits and will be expanded to 7000 qubits during 2023–2024,with remarkable improvements in decoherence and topology.This machine is expected to promote the solution of large-scale combinatorial optimization problems.One of the contributions of this paper is the discussion of the long-term impact of D-Wave on the development of post-quantum cryptography standards.

An asymptotically optimal public parking lot location algorithm based on intuitive reasoning

In order to solve the problems of road traffic congestion and the increasing parking time caused by the imbalance of parking lot supply and demand,this paper proposes an asymptotically optimal public parking lot location algorithm based on intuitive reasoning to optimize the parking lot location problem.Guided by the idea of intuitive reasoning,we use walking distance as indicator to measure the variability among location data and build a combinatorial optimization model aimed at guiding search decisions in the solution space of complex problems to find optimal solutions.First,Selective Attention Mechanism(SAM)is introduced to reduce the search space by adaptively focusing on the important information in the features.Then,Quantum Annealing(QA)algorithm with quantum tunneling effect is used to jump out of the local extremum in the search space with high probability and further approach the global optimal solution.Experiments on the parking lot location dataset in Luohu District,Shenzhen,show that the proposed method has improved the accuracy and running speed of the solution,and the asymptotic optimality of the algorithm and its effectiveness in solving the public parking lot location problem are verified.