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Известия Южного федерального университета. Технические науки

Способ организации ветвления в квантовых вычислениях

Vyacheslav F. Guzik, С. М. Гушанский, Евсеев Олег Константинович

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Quantum computation can be used to solve NP-tasks, but it does not allow using classical manner of algorithmic organization of the solving task. The offered article describes a method of enhancing the abilities of quantum computations process by adding the fourth step to its three ordinary steps (initialization, computation, measurement. A variant of the adding the step of analysis of temporarily saved state of the system and branching the program of controlling influences comparatively to its result is considered.

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The new model of quantum computation is proposed, for which an effective algorithm of solving any task in NP is described. The work is based and inspired be the Grover's algorithm for solving NP-tasks with quadratic speedup compared to the classical computation model. The provided model and algorithm exhibit the exponential speedup over that described by Grover.

arXiv:1401.6030•Jan 23, 2014•1 citation

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The paper presents the principles of operation of quantum computers. Competitive advantages of quantum computing are shown and some variants of a construction of an ideal quantum computer proposed. We analyze also the computational process in a quantum computer from the point of view of the complexity of algorithms. Implementation of nodes of a quantum computer is exemplified based on quantum communication schemes. The operation of Bloch sphere and visualization of the state of the qubit are described. Major obstacles to the creation of quantum computers are considered.

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Optimal Solving of a Scheduling Problem Using Quantum Annealing Metaheuristics on the D-Wave Quantum Solver

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Accurately solving discrete optimization problems is still a serious challenge for classical computing systems. Despite significant progress, it is still impossible to optimally solve examples of the size found in real-world applications. This article examines the problem of scheduling tasks on one machine. Each task has an associated execution time, desired completion date, and a late penalty feature weight. The order of executing tasks should be determined in a manner that minimizes the sum of delay costs. Despite the simplicity of the formulation, this problem is NP-hard and is representative of optimization challenges encountered in the practice of production control, management, and logistics.In this work, we propose using a quantum computing environment to solve it. The main disadvantage of calculations on quantum computers is their nondeterminism. Therefore, there is no guarantee of optimality of solutions to discrete optimization problems determined on a quantum computer.We propose a novel approach to constructing hybrid algorithms that guarantee the optimality of the solution. The algorithm for solving the task scheduling problem considered here is based on the branch and bound method. Calculations are performed alternately on a classical computer and a quantum computer. The lower and upper bounds of the criterion function are determined on a quantum computer. Computational experiments were performed on the D-Wave quantum computer. In small examples, the algorithm runs faster and generates significantly fewer solution tree vertices than its counterpart running on a classic computer. For larger examples, the proposed runtime-constrained method, acting as a heuristic, is an interesting alternative to using quantum computing hardware in relation to classical approaches based on silicon computers.

IEEE Transactions on Systems Man and Cybernetics Systems•Oct 2, 2024•22 citations

Ускорение моделирования квантовых вычислений с применением аппаратных ускорителей и распределенных вычислений

Гузик Вячеслав Филиппович, Гушанский Сергей Михайлович, Кубраков Евгений Сергеевич

In the past few decades the problem of creating quantum computer is one of the most important. Quantum computer uses the quantum mechanics such as quantum parallelism and quantum entanglement. Using this mechanisms quantum computer is able to solve some of the problems of NP-class in polynomial time. In our days the prototypes of such class of devices are created, but they cant be used for effective solving of the planned problems because of difficulties of realization. However, mathematical apparatus that describes the behavior of quantum particles using wave function exists. This apparatus allows creating algorithms that can be effectively solved only on quantum computer. Hence its a problem of investigation of effectiveness of new quantum algorithms. The only option is modeling quantum system on classical devices. But the quantum system cant be modeled effectively on classical devices, hence its suggested to use methodic of accelerating of modeling of quantum computing.

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Integer Quadratic Programming for Control and Communication

Daniel Axehill

The main topic of this thesis is integer quadratic programming with applications to problems arising in the areas of automatic control and communication. One of the most widespread modern control methods is Model Predictive Control (MPC). In each sampling time, MPC requires the solution of a Quadratic Programming (QP) problem. To be able to use MPC for large systems, and at high sampling rates, optimization routines tailored for MPC are used. In recent years, the range of application of MPC has been extended to so-called hybrid systems. Hybrid systems are systems where continuous dynamics interact with logic. When this extension is made, binary variables are introduced in the problem. As a consequence, the QP problem has to be replaced by a far more challenging Mixed Integer Quadratic Programming (MIQP) problem, which is known to have a computational complexity which grows exponentially in the number of binary optimization variables. In modern communication systems, multiple users share a so-called multi-access channel. To estimate the information originally sent, a maximum likelihood problem involving binary variables can be solved. The process of simultaneously estimating the information sent by multiple users is called Multiuser Detection (MUD). In this thesis, the problem to efficiently solve MIQP problems originating from MPC and MUD is addressed. Four different algorithms are presented. First, a polynomial complexity preprocessing algorithm for binary quadratic programming problems is presented. By using the algorithm, some, or all, binary variables can be computed efficiently already in the preprocessing phase. In numerical experiments, the algorithm is applied to unconstrained MPC problems with a mixture of real valued and binary valued control signals, and the result shows that the performance gain can be significant compared to solving the problem using branch and bound. The preprocessing algorithm has also been applied to the MUD problem, where simulations have shown that the bit error rate can be significantly reduced compared to using common suboptimal algorithms. Second, an MIQP algorithm tailored for MPC is presented. The algorithm uses a branch and bound method where the relaxed node problems are solved by a dual active set QP algorithm. In this QP algorithm, the KKT systems are solved using Riccati recursions in order to decrease the computational complexity. Simulation results show that both the proposed QP solver and MIQP solver have lower computational complexity compared to corresponding generic solvers. Third, the dual active set QP algorithm is enhanced using ideas from gradient projection methods. The performance of this enhanced algorithm is shown to be comparable with the existing commercial state-of-the-art QP solver \\cplex for some random linear MPC problems. Fourth, an algorithm for efficient computation of the search directions in an SDP solver for a proposed alternative SDP relaxation applicable to MPC problems with binary control signals is presented. The SDP relaxation considered has the potential to give a tighter lower bound on the optimal objective function value compared to the QP relaxation that is traditionally used in branch and bound for these problems, and its computational performance is better than the ordinary SDP relaxation for the problem. Furthermore, the tightness of the different relaxations is investigated both theoretically and in numerical experiments.

•Jan 1, 2008•74 citations

Software model of a computer with a quantum coprocessor

Mikhail Kirilyuk, Nikolay Paramonov, Konstantin Suminov

Background. The object of the study is specialized computing systems containing a quantum coprocessor. The subject of the study is the process of organizing calculations in specialized computing systems, taking into account the interaction of quantum and classical computers. The purpose of the work is to evaluate the effectiveness of solving computationally complex problems using specialized computing systems with a quantum coprocessor by developing a software model of a computing complex that includes a quantum coprocessor. Materials and methods. Studies of the process of organizing calculations in specialized computing systems, taking into account the interaction of quantum and classical computers, were carried out using simulation and experimental methods. Results. A software model has been developed. The software model of the computing complex, which includes a quantum coprocessor, is made in the form of a set of experimental programs and placed on a modeling stand based on the Russian hardware and software platform “Elbrus”. The developed software package consists of three parts: interface, computing and web applications. Conclusions. Using the developed software model placed on the simulation stand, estimates of the efficiency of solving a number of problems using a quantum coprocessor were obtained. It is shown that for some tasks the acceleration obtained using a quantum coprocessor can reach exponential levels.

Известия высших учебных заведений. Поволжский регион. Технические науки•Jan 1, 2023•0 citations
Quantum computation can be used to solve NP-tasks, but it does not allow using classical manner of algorithmic organization of the solving task. The offered article describes a method of enhancing the abilities of quantum computations process by adding the fourth step to its three ordinary steps (initialization, computation, measurement. A variant of the adding the step of analysis of temporarily saved state of the system and branching the program of controlling influences comparatively to its result is considered.
The paper presents the principles of operation of quantum computers. Competitive advantages of quantum computing are shown and some variants of a construction of an ideal quantum computer proposed. We analyze also the computational process in a quantum computer from the point of view of the complexity of algorithms. Implementation of nodes of a quantum computer is exemplified based on quantum communication schemes. The operation of Bloch sphere and visualization of the state of the qubit are described. Major obstacles to the creation of quantum computers are considered.
Accurately solving discrete optimization problems is still a serious challenge for classical computing systems. Despite significant progress, it is still impossible to optimally solve examples of the size found in real-world applications. This article examines the problem of scheduling tasks on one machine. Each task has an associated execution time, desired completion date, and a late penalty feature weight. The order of executing tasks should be determined in a manner that minimizes the sum of delay costs. Despite the simplicity of the formulation, this problem is NP-hard and is representative of optimization challenges encountered in the practice of production control, management, and logistics.In this work, we propose using a quantum computing environment to solve it. The main disadvantage of calculations on quantum computers is their nondeterminism. Therefore, there is no guarantee of optimality of solutions to discrete optimization problems determined on a quantum computer.We propose a novel approach to constructing hybrid algorithms that guarantee the optimality of the solution. The algorithm for solving the task scheduling problem considered here is based on the branch and bound method. Calculations are performed alternately on a classical computer and a quantum computer. The lower and upper bounds of the criterion function are determined on a quantum computer. Computational experiments were performed on the D-Wave quantum computer. In small examples, the algorithm runs faster and generates significantly fewer solution tree vertices than its counterpart running on a classic computer. For larger examples, the proposed runtime-constrained method, acting as a heuristic, is an interesting alternative to using quantum computing hardware in relation to classical approaches based on silicon computers.
In the past few decades the problem of creating quantum computer is one of the most important. Quantum computer uses the quantum mechanics such as quantum parallelism and quantum entanglement. Using this mechanisms quantum computer is able to solve some of the problems of NP-class in polynomial time. In our days the prototypes of such class of devices are created, but they cant be used for effective solving of the planned problems because of difficulties of realization. However, mathematical apparatus that describes the behavior of quantum particles using wave function exists. This apparatus allows creating algorithms that can be effectively solved only on quantum computer. Hence its a problem of investigation of effectiveness of new quantum algorithms. The only option is modeling quantum system on classical devices. But the quantum system cant be modeled effectively on classical devices, hence its suggested to use methodic of accelerating of modeling of quantum computing.
The main topic of this thesis is integer quadratic programming with applications to problems arising in the areas of automatic control and communication. One of the most widespread modern control methods is Model Predictive Control (MPC). In each sampling time, MPC requires the solution of a Quadratic Programming (QP) problem. To be able to use MPC for large systems, and at high sampling rates, optimization routines tailored for MPC are used. In recent years, the range of application of MPC has been extended to so-called hybrid systems. Hybrid systems are systems where continuous dynamics interact with logic. When this extension is made, binary variables are introduced in the problem. As a consequence, the QP problem has to be replaced by a far more challenging Mixed Integer Quadratic Programming (MIQP) problem, which is known to have a computational complexity which grows exponentially in the number of binary optimization variables. In modern communication systems, multiple users share a so-called multi-access channel. To estimate the information originally sent, a maximum likelihood problem involving binary variables can be solved. The process of simultaneously estimating the information sent by multiple users is called Multiuser Detection (MUD). In this thesis, the problem to efficiently solve MIQP problems originating from MPC and MUD is addressed. Four different algorithms are presented. First, a polynomial complexity preprocessing algorithm for binary quadratic programming problems is presented. By using the algorithm, some, or all, binary variables can be computed efficiently already in the preprocessing phase. In numerical experiments, the algorithm is applied to unconstrained MPC problems with a mixture of real valued and binary valued control signals, and the result shows that the performance gain can be significant compared to solving the problem using branch and bound. The preprocessing algorithm has also been applied to the MUD problem, where simulations have shown that the bit error rate can be significantly reduced compared to using common suboptimal algorithms. Second, an MIQP algorithm tailored for MPC is presented. The algorithm uses a branch and bound method where the relaxed node problems are solved by a dual active set QP algorithm. In this QP algorithm, the KKT systems are solved using Riccati recursions in order to decrease the computational complexity. Simulation results show that both the proposed QP solver and MIQP solver have lower computational complexity compared to corresponding generic solvers. Third, the dual active set QP algorithm is enhanced using ideas from gradient projection methods. The performance of this enhanced algorithm is shown to be comparable with the existing commercial state-of-the-art QP solver \\cplex for some random linear MPC problems. Fourth, an algorithm for efficient computation of the search directions in an SDP solver for a proposed alternative SDP relaxation applicable to MPC problems with binary control signals is presented. The SDP relaxation considered has the potential to give a tighter lower bound on the optimal objective function value compared to the QP relaxation that is traditionally used in branch and bound for these problems, and its computational performance is better than the ordinary SDP relaxation for the problem. Furthermore, the tightness of the different relaxations is investigated both theoretically and in numerical experiments.
Background. The object of the study is specialized computing systems containing a quantum coprocessor. The subject of the study is the process of organizing calculations in specialized computing systems, taking into account the interaction of quantum and classical computers. The purpose of the work is to evaluate the effectiveness of solving computationally complex problems using specialized computing systems with a quantum coprocessor by developing a software model of a computing complex that includes a quantum coprocessor. Materials and methods. Studies of the process of organizing calculations in specialized computing systems, taking into account the interaction of quantum and classical computers, were carried out using simulation and experimental methods. Results. A software model has been developed. The software model of the computing complex, which includes a quantum coprocessor, is made in the form of a set of experimental programs and placed on a modeling stand based on the Russian hardware and software platform “Elbrus”. The developed software package consists of three parts: interface, computing and web applications. Conclusions. Using the developed software model placed on the simulation stand, estimates of the efficiency of solving a number of problems using a quantum coprocessor were obtained. It is shown that for some tasks the acceleration obtained using a quantum coprocessor can reach exponential levels.