scholarly journals Quantum-accelerated constraint programming

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 550
Author(s):  
Kyle E. C. Booth ◽  
Bryan O'Gorman ◽  
Jeffrey Marshall ◽  
Stuart Hadfield ◽  
Eleanor Rieffel
Keyword(s):  
Constraint Programming ◽  
Optimization Problems ◽  
Fault Tolerant ◽  
Quantum Algorithms ◽  
Global Constraints ◽  
Quantum Computers ◽  
Promising Candidate ◽  
Backtracking Search ◽  
Combinatorial Optimization Problems ◽  
Classical Quantum

Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking tree search augmented with logical inference. In this paper, we show how quantum algorithms can accelerate CP, at both the levels of inference and search. Leveraging existing quantum algorithms, we introduce a quantum-accelerated filtering algorithm for the alldifferent global constraint and discuss its applicability to a broader family of global constraints with similar structure. We propose frameworks for the integration of quantum filtering algorithms within both classical and quantum backtracking search schemes, including a novel hybrid classical-quantum backtracking search method. This work suggests that CP is a promising candidate application for early fault-tolerant quantum computers and beyond.

scholarly journals Global constraints in modeling and solving problems within the Constraint Programming paradigm.

2020 ◽  
Vol 11 (8-2020) ◽  
pp. 67-83
Author(s):  
Yu.A. Oleynik ◽  
◽  
A.A. Zuenko ◽  
Keyword(s):  
Constraint Programming ◽  
High Performance ◽  
Optimization Problems ◽  
Building Blocks ◽  
Global Constraints ◽  
Combinatorial Search ◽  
Combinatorial Optimization Problems ◽  
Programming Paradigm ◽  
Moment Constraint ◽  
The Moment

At the moment, constraint programming technology is a powerful tool for solving combinatorial search and combinatorial optimization problems. To use this technology, any task must be formulated as a task of satisfying constraints. The role of the concept of global constraints in modeling and solving applied problems within the framework of the constraint programming paradigm can hardly be overestimated. The procedures that implement the algorithms of filtering global constraints are the elementary “building blocks” from which the model of a specific applied problem is built. Algorithms for filtering global constraints, as a rule, are supported by the corresponding developed theories that allow organizing high-performance computing. The choice of a particular software library is primarily determined by the extent to which the set and method of implementing global constraints corresponds tothe level of modern research in this area. The main focus of this article is focused on an overview of global constraints that are implemented within the most popular constraint programming libraries: Choco, GeCode, JaCoP, MiniZinc.

scholarly journals Applying Quantum Optimization Algorithms for Linear Programming

2017 ◽  
Author(s):  
Mert Side ◽  
Volkan Erol
Keyword(s):  
Resource Allocation ◽  
Linear Programming ◽  
Production Scheduling ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Quantum Optimization ◽  
Special Case

Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we looked at the duality of resource allocation problems. First, we chose a real world optimization problem and looked at its solution with linear programming. Then, we restudied this problem with a quantum algorithm in order to understand whether if there is a speedup of the solution. The improvement in computation is analysed and some interesting results are reported.

scholarly journals Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 553
Author(s):  
Xiao Xiao ◽  
J. K. Freericks ◽  
A. F. Kemper
Keyword(s):  
Phase Diagrams ◽  
Fault Tolerant ◽  
Quantum Algorithms ◽  
Entanglement Entropy ◽  
Quantum Phase ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Model ◽  
Quantum Properties ◽  
Topological Quantum

Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated, also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundaries. We show how maintaining particle-hole symmetry when sampling through the Brillouin zone is critical to obtaining high accuracy. This work illustrates how topological protection intrinsic to a quantum model can be employed to perform robust calculations on NISQ hardware, when one measures the appropriate protected quantum properties. It opens the door for further simulation of topological quantum models on quantum hardware available today.

scholarly journals Quantum Algorithms for Solving Ordinary Differential Equations via Classical Integration Methods

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 502
Author(s):  
Benjamin Zanger ◽  
Christian B. Mendl ◽  
Martin Schulz ◽  
Martin Schreiber
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Optimization Problems ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
High Order ◽  
Quantum Computers ◽  
Integration Methods ◽  
Linear Ordinary Differential Equations ◽  
Legendre Collocation Method

Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis encoding and fixed-point arithmetic on a digital quantum computer, and (ii) representing and solving high-order Runge-Kutta methods as optimization problems on quantum annealers. As realizations applied to two-dimensional linear ordinary differential equations, we devise and simulate corresponding digital quantum circuits, and implement and run a 6th order Gauss-Legendre collocation method on a D-Wave 2000Q system, showing good agreement with the reference solution. We find that the quantum annealing approach exhibits the largest potential for high-order implicit integration methods. As promising future scenario, the digital arithmetic method could be employed as an "oracle" within quantum search algorithms for inverse problems.

scholarly journals Applying Quantum Optimization Algorithms for Linear Programming

2017 ◽  
Author(s):  
Mert Side ◽  
Volkan Erol
Keyword(s):  
Resource Allocation ◽  
Linear Programming ◽  
Production Scheduling ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Quantum Optimization ◽  
Special Case

Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we looked at the duality of resource allocation problems. First, we chose a real world optimization problem and looked at its solution with linear programming. Then, we restudied this problem with a quantum algorithm in order to understand whether if there is a speedup of the solution. The improvement in computation is analysed and some interesting results are reported.

scholarly journals Solving Combinatorial Optimization Problems on Quantum Computers

2020 ◽  
pp. 5-13
Author(s):  
Vyacheslav Korolyov ◽  
Oleksandr Khodzinskyi
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Quantum Computer ◽  
Independent Set ◽  
Cloud Services ◽  
Quantum Computers ◽  
Maximal Independent Set ◽  
Maximum Independent Set ◽  
Combinatorial Optimization Problems ◽  
D Wave

Introduction. Quantum computers provide several times faster solutions to several NP-hard combinatorial optimization problems in comparison with computing clusters. The trend of doubling the number of qubits of quantum computers every year suggests the existence of an analog of Moore's law for quantum computers, which means that soon they will also be able to get a significant acceleration of solving many applied large-scale problems. The purpose of the article is to review methods for creating algorithms of quantum computer mathematics for combinatorial optimization problems and to analyze the influence of the qubit-to-qubit coupling and connections strength on the performance of quantum data processing. Results. The article offers approaches to the classification of algorithms for solving these problems from the perspective of quantum computer mathematics. It is shown that the number and strength of connections between qubits affect the dimensionality of problems solved by algorithms of quantum computer mathematics. It is proposed to consider two approaches to calculating combinatorial optimization problems on quantum computers: universal, using quantum gates, and specialized, based on a parameterization of physical processes. Examples of constructing a half-adder for two qubits of an IBM quantum processor and an example of solving the problem of finding the maximum independent set for the IBM and D-wave quantum computers are given. Conclusions. Today, quantum computers are available online through cloud services for research and commercial use. At present, quantum processors do not have enough qubits to replace semiconductor computers in universal computing. The search for a solution to a combinatorial optimization problem is performed by achieving the minimum energy of the system of coupled qubits, on which the task is mapped, and the data are the initial conditions. Approaches to solving combinatorial optimization problems on quantum computers are considered and the results of solving the problem of finding the maximum independent set on the IBM and D-wave quantum computers are given. Keywords: quantum computer, quantum computer mathematics, qubit, maximal independent set for a graph.

scholarly journals On the Representation of Boolean and Real Functions as Hamiltonians for Quantum Computing

2021 ◽  
Vol 2 (4) ◽  
pp. 1-21
Author(s):  
Stuart Hadfield
Keyword(s):  
Quantum Computing ◽  
Boolean Functions ◽  
Optimization Problems ◽  
Quantum Algorithms ◽  
Building Blocks ◽  
Constraint Satisfaction Problems ◽  
Boolean Formula ◽  
Combinatorial Optimization Problems ◽  
Compute Function ◽  
Real Functions

Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate optimization algorithm to combinatorial optimization problems. We show how such functions are naturally represented by Hamiltonians given as sums of Pauli Z operators (Ising spin operators) with the terms of the sum corresponding to the function’s Fourier expansion. For many classes of Boolean functions which are given by a compact description, such as a Boolean formula in conjunctive normal form that gives an instance of the satisfiability problem, it is #P-hard to compute its Hamiltonian representation, i.e., as hard as computing its number of satisfying assignments. On the other hand, no such difficulty exists generally for constructing Hamiltonians representing a real function such as a sum of local Boolean clauses each acting on a fixed number of bits as is common in constraint satisfaction problems. We show composition rules for explicitly constructing Hamiltonians representing a wide variety of Boolean and real functions by combining Hamiltonians representing simpler clauses as building blocks, which are particularly suitable for direct implementation as classical software. We further apply our results to the construction of controlled-unitary operators, and to the special case of operators that compute function values in an ancilla qubit register. Finally, we outline several additional applications and extensions of our results to quantum algorithms for optimization. A goal of this work is to provide a design toolkit for quantum optimization which may be utilized by experts and practitioners alike in the construction and analysis of new quantum algorithms, and at the same time to provide a unified framework for the various constructions appearing in the literature.

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