Quantum Computing for Solving Spatial Optimization Problems

2020 ◽  
pp. 97-113
Author(s):  
Mengyu Guo ◽  
Shaowen Wang
Keyword(s):  
Quantum Computing ◽  
Optimization Problems ◽  
Spatial Optimization

Reinforcement-Learning-Based Quantum Adiabatic Algorithm Design for Integer Programming

SPIN ◽  
2021 ◽  
Author(s):  
Jiawei Zhu
Keyword(s):  
Quantum Computing ◽  
Reinforcement Learning ◽  
Integer Programming ◽  
Learning Process ◽  
Optimization Problems ◽  
Algorithm Design ◽  
Hamiltonian Path ◽  
Quantum Algorithm ◽  
Learning Approach ◽  
Computation Efficiency

Adiabatic quantum computing (AQC) is a computation protocol to solve difficult problems exploiting quantum advantage, directly applicable to optimization problems. In performing the AQC, different configurations of the Hamiltonian path could lead to dramatic differences in the computation efficiency. It is thus crucial to configure the Hamiltonian path to optimize the computation performance of AQC. Here we apply a reinforcement learning approach to configure AQC for integer programming, where we find the learning process automatically converges to a quantum algorithm that exhibits scaling advantage over the trivial AQC using a linear Hamiltonian path. This reinforcement-learning-based approach for quantum adiabatic algorithm design for integer programming can well be adapted to the quantum resources in different quantum computation devices, due to its built-in flexibility.

GENETIC ALGORITHMS AND OPTIMIZATION PROBLEMS IN QUANTUM COMPUTING

2010 ◽  
Vol 21 (11) ◽  
pp. 1359-1375 ◽  
Author(s):  
Y. HARDY ◽  
W.-H. STEEB
Keyword(s):  
Genetic Algorithms ◽  
Quantum Computing ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Data Type ◽  
Entangled States ◽  
Chsh Inequality ◽  
Entanglement Measures

We solve a number of problems in quantum computing by applying genetic algorithms. We use the bitset class of C ++ to represent any data type for genetic algorithms. Thus we have a flexible way to solve any optimization problem. The Bell-CHSH inequality and entanglement measures are studied using genetic algorithms. Entangled states form the backbone for teleportation. The C ++ code is also provided.

scholarly journals Feature Selection for Recommender Systems with Quantum Computing

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 970
Author(s):  
Riccardo Nembrini ◽  
Maurizio Ferrari Dacrema ◽  
Paolo Cremonesi
Keyword(s):  
Feature Selection ◽  
Quantum Computing ◽  
Recommender Systems ◽  
Domain Knowledge ◽  
Optimization Problems ◽  
Quantum Computer ◽  
Mathematical Formulation ◽  
Easy Access ◽  
Quantum Computers ◽  
User Interactions

The promise of quantum computing to open new unexplored possibilities in several scientific fields has been long discussed, but until recently the lack of a functional quantum computer has confined this discussion mostly to theoretical algorithmic papers. It was only in the last few years that small but functional quantum computers have become available to the broader research community. One paradigm in particular,quantum annealing, can be used to sample optimal solutions for a number of NP-hard optimization problems represented with classical operations research tools, providing an easy access to the potential of this emerging technology. One of the tasks that most naturally fits in this mathematical formulation is feature selection. In this paper, we investigate how to design a hybrid feature selection algorithm for recommender systems that leverages the domain knowledge and behavior hidden in the user interactions data. We represent the feature selection as an optimization problem and solve it on a real quantum computer, provided by D-Wave. The results indicate that the proposed approach is effective in selecting a limited set of important features and that quantum computers are becoming powerful enough to enter the wider realm of applied science.

scholarly journals Why We Should Be Skeptical of Quantum Computing

2021 ◽  
Author(s):  
Alan Kadin
Keyword(s):  
Quantum Computing ◽  
Quantum Entanglement ◽  
Degrees Of Freedom ◽  
Optimization Problems ◽  
Electronic Energy ◽  
Excess Noise ◽  
Energy Bands ◽  
Coupled Modes ◽  
Classical Computing ◽  
Electronic Energy Bands

<div>It is widely believed that quantum computing is on the threshold of practicality, with performance that will soon greatly surpass that of classical computing. On the contrary, I argue that quantum computing does not currently exist, and probably never will. First, although quantum annealing systems have been demonstrated to solve practical optimization problems, they are actually performing classical analog annealing, with no quantum enhancement. In contrast, while systems of quantum gate arrays, which are expected to perform digital quantum computing, have been fabricated with up to ~ 100 qubits in several technologies, they have not performed any practical computations. This is not merely a question of excess noise; the theory of massive quantum entanglement, necessary for the desired performance, has never been actually been verified. The well-established quantum results such as electronic energy bands do not incorporate quantum entanglement. I suggest that the experimental observations in multi-qubit systems may be explained as the result of delocalized coupled oscillator modes, similar to that in electronic energy bands. Such coupled modes would not yield the exponential increase in degrees of freedom needed for quantum speedup, and hence would not be useful for computing. Tests on these multi-qubit systems should be able to distinguish these two models. The quantum computing research community really needs to address this issue.</div>

scholarly journals Sweeping quantum annealing algorithm for constrained optimization problems

2021 ◽  
Author(s):  
Zheng Yan ◽  
Zheng Zhou ◽  
Yancheng Wang ◽  
ZiYang Meng ◽  
Xue-Feng Zhang
Keyword(s):  
Quantum Computing ◽  
Thermal Annealing ◽  
Optimization Problems ◽  
Material Design ◽  
Quantum Annealing ◽  
Constrained Problems ◽  
Annealing Algorithm ◽  
Computing Platforms ◽  
Annealing Algorithms ◽  
Promising Avenue

Abstract As a typical quantum computing algorithm, quantum annealing is widely used in the optimization of glass-like problems to find the best solution. However, the optimization problems in constrained complex systems usually involve topological structures, and the performance of the quantum annealing algorithm is still largely unknown. Here, we take an Ising system as a typical example with local constraints accompanied by intrinsic topological properties that can be implemented on quantum computing platforms such as the D-wave machine, and study the effectiveness of the quantum annealing algorithm in its optimization and compare it with that of the thermal annealing. We find that although conventional quantum annealing is difficult for the optimization of constrained topological problems, a generalized algorithm --- the sweeping quantum annealing method --- can be designed and solve the problem with better efficiency than both conventional quantum and thermal annealing algorithms. The sweeping quantum annealing algorithm, therefore, opens up a promising avenue for quantum computing of constrained problems and can be readily employed on the optimizations in quantum material design, engineering, and even social sciences.

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.

scholarly journals Influence of Probability of Variation Operator on the Performance of Quantum-Inspired Evolutionary Algorithm for 0/1 Knapsack Problem

2010 ◽  
Vol 4 (1) ◽  
pp. 37-48
Author(s):  
Mozammel H.A. Khan
Keyword(s):  
Genetic Algorithm ◽  
Quantum Computing ◽  
Combinatorial Optimization ◽  
Evolutionary Algorithm ◽  
Knapsack Problem ◽  
Optimization Problems ◽  
Exploration And Exploitation ◽  
Good Balance ◽  
Combinatorial Optimization Problems ◽  
Variation Operator

Quantum-Inspired Evolutionary Algorithm (QEA) has been shown to be better performing than classical Genetic Algorithm based evolutionary techniques for combinatorial optimization problems like 0/1 knapsack problem. QEA uses quantum computing-inspired representation of solution called Q-bit individual consisting of Q-bits. The probability amplitudes of the Q-bits are changed by application of Q-gate operator, which is classical analogous of quantum rotation operator. The Q-gate operator is the only variation operator used in QEA, which along with some problem specific heuristic provides exploitation of the properties of the best solutions. In this paper, we analyzed the characteristics of the QEA for 0/1 knapsack problem and showed that a probability in the range 0.3 to 0.4 for the application of the Q-gate variation operator has the greatest likelihood of making a good balance between exploration and exploitation. Experimental results agree with the analytical finding.

scholarly journals Why We Should Be Skeptical of Quantum Computing

2021 ◽  
Author(s):  
Alan Kadin
Keyword(s):  
Quantum Computing ◽  
Quantum Entanglement ◽  
Degrees Of Freedom ◽  
Optimization Problems ◽  
Electronic Energy ◽  
Excess Noise ◽  
Energy Bands ◽  
Coupled Modes ◽  
Classical Computing ◽  
Electronic Energy Bands

<div>It is widely believed that quantum computing is on the threshold of practicality, with performance that will soon greatly surpass that of classical computing. On the contrary, I argue that quantum computing does not currently exist, and probably never will. First, although quantum annealing systems have been demonstrated to solve practical optimization problems, they are actually performing classical analog annealing, with no quantum enhancement. In contrast, while systems of quantum gate arrays, which are expected to perform digital quantum computing, have been fabricated with up to ~ 100 qubits in several technologies, they have not performed any practical computations. This is not merely a question of excess noise; the theory of massive quantum entanglement, necessary for the desired performance, has never been actually been verified. The well-established quantum results such as electronic energy bands do not incorporate quantum entanglement. I suggest that the experimental observations in multi-qubit systems may be explained as the result of delocalized coupled oscillator modes, similar to that in electronic energy bands. Such coupled modes would not yield the exponential increase in degrees of freedom needed for quantum speedup, and hence would not be useful for computing. Tests on these multi-qubit systems should be able to distinguish these two models. The quantum computing research community really needs to address this issue.</div>

A benchmark for quantum optimization: the traveling salesman

2021 ◽  
Vol 21 (7&8) ◽  
pp. 557-562
Author(s):  
Richard H. Warren
Keyword(s):  
Quantum Computing ◽  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Traveling Salesman Problems ◽  
Combinatorial Optimization Problems ◽  
Quantum Optimization

We present compelling reasons for symmetric traveling salesman problems (TSPs) to be the benchmark for quantum computing of combinatorial optimization problems for all types of quantum hardware. There are seven reasons for endorsing these TSPs to be the benchmark and no shortcomings.

Sign in / Sign up

Export Citation Format

Share Document