1,397 research outputs found
A quantum-inspired tensor network method for constrained combinatorial optimization problems
Combinatorial optimization is of general interest for both theoretical study
and real-world applications. Fast-developing quantum algorithms provide a
different perspective on solving combinatorial optimization problems. In this
paper, we propose a quantum inspired algorithm for general locally constrained
combinatorial optimization problems by encoding the constraints directly into a
tensor network state. The optimal solution can be efficiently solved by
borrowing the imaginary time evolution from a quantum many-body system. We
demonstrate our algorithm with the open-pit mining problem numerically. Our
computational results show the effectiveness of this construction and potential
applications in further studies for general combinatorial optimization
problems
Natural evolution strategies and variational Monte Carlo
A notion of quantum natural evolution strategies is introduced, which
provides a geometric synthesis of a number of known quantum/classical
algorithms for performing classical black-box optimization. Recent work of
Gomes et al. [2019] on heuristic combinatorial optimization using neural
quantum states is pedagogically reviewed in this context, emphasizing the
connection with natural evolution strategies. The algorithmic framework is
illustrated for approximate combinatorial optimization problems, and a
systematic strategy is found for improving the approximation ratios. In
particular it is found that natural evolution strategies can achieve
approximation ratios competitive with widely used heuristic algorithms for
Max-Cut, at the expense of increased computation time
A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering
Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD
Quantum computing for finance
Quantum computers are expected to surpass the computational capabilities of
classical computers and have a transformative impact on numerous industry
sectors. We present a comprehensive summary of the state of the art of quantum
computing for financial applications, with particular emphasis on stochastic
modeling, optimization, and machine learning. This Review is aimed at
physicists, so it outlines the classical techniques used by the financial
industry and discusses the potential advantages and limitations of quantum
techniques. Finally, we look at the challenges that physicists could help
tackle
Quantum Approximate Optimization Algorithm Parameter Prediction Using a Convolutional Neural Network
The Quantum approximate optimization algorithm (QAOA) is a quantum-classical
hybrid algorithm aiming to produce approximate solutions for combinatorial
optimization problems. In the QAOA, the quantum part prepares a quantum
parameterized state that encodes the solution, where the parameters are
optimized by a classical optimizer. However, it is difficult to find optimal
parameters when the quantum circuit becomes deeper. Hence, there is numerous
active research on the performance and the optimization cost of QAOA. In this
work, we build a convolutional neural network to predict parameters of depth
QAOA instance by the parameters from the depth QAOA counterpart. We propose two
strategies based on this model. First, we recurrently apply the model to
generate a set of initial values for a certain depth QAOA. It successfully
initiates depth 10 QAOA instances, whereas each model is only trained with the
parameters from depths less than 6. Second, the model is applied repetitively
until the maximum expected value is reached. An average approximation ratio of
0.9759 for Max-Cut over 264 Erd\H{o}s-R\'{e}nyi graphs is obtained, while the
optimizer is only adopted for generating the first input of the model.Comment: 9 pages, 4 figures, 1 table
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