Quantum Optimization and Machine Learning

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (15 September 2021) | Viewed by 9409

Special Issue Editor

School of Industrial and Systems Engineering, The University of Oklahoma, Norman, OK 73019, USA
Interests: operations research/management science; mathematical programming; interior point methods; multiobjective optimization; control theory; computational and algebraic geometry; artificial neural networks; kernel methods; evolutionary programming; global optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Papers related to the theory of quantum optimization and applications are welcomed. Special interest will be given to global optimization, but any other quantum optimization algorithm will fit this Special Issue. Applications of quantum optimization in machine learning and big data are also welcome.

Quantum computation provides tools to solve two broad classes of optimization problems: Semi-definite programming (SDP) and constraint satisfaction problems (CSPs). For example, in 2016, a quantum algorithm for SDP was developed that is quadratically faster in the number of constraints and variables. SDP finds a number of applications in machine learning. The quantum approximate optimization algorithm and the quantum adiabatic algorithm are known for CSPs. New problems related with machine learning require more efficient optimization algorithms to handle big data.

Prof. Theodore B. Trafalis
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

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Keywords

  • Quantum computing
  • Optimization
  • Machine Learning

Published Papers (3 papers)

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Research

21 pages, 494 KiB  
Article
Globally Optimizing QAOA Circuit Depth for Constrained Optimization Problems
by Rebekah Herrman, Lorna Treffert, James Ostrowski, Phillip C. Lotshaw, Travis S. Humble and George Siopsis
Algorithms 2021, 14(10), 294; https://doi.org/10.3390/a14100294 - 11 Oct 2021
Cited by 9 | Viewed by 1896
Abstract
We develop a global variable substitution method that reduces n-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to 3-SAT and analyze the optimal quantum unitary circuit depth needed to solve the reduced [...] Read more.
We develop a global variable substitution method that reduces n-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to 3-SAT and analyze the optimal quantum unitary circuit depth needed to solve the reduced problem using the quantum approximate optimization algorithm. For benchmark 3-SAT problems, we find that the upper bound of the unitary circuit depth is smaller when the problem is formulated as a product and uses the substitution method to decompose gates than when the problem is written in the linear formulation, which requires no decomposition. Full article
(This article belongs to the Special Issue Quantum Optimization and Machine Learning)
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27 pages, 5102 KiB  
Article
qRobot: A Quantum Computing Approach in Mobile Robot Order Picking and Batching Problem Solver Optimization
by Parfait Atchade-Adelomou, Guillermo Alonso-Linaje, Jordi Albo-Canals and Daniel Casado-Fauli
Algorithms 2021, 14(7), 194; https://doi.org/10.3390/a14070194 - 26 Jun 2021
Cited by 18 | Viewed by 4080
Abstract
This article aims to bring quantum computing to robotics. A quantum algorithm is developed to minimize the distance traveled in warehouses and distribution centers where order picking is applied. For this, a proof of concept is proposed through a Raspberry Pi 4, generating [...] Read more.
This article aims to bring quantum computing to robotics. A quantum algorithm is developed to minimize the distance traveled in warehouses and distribution centers where order picking is applied. For this, a proof of concept is proposed through a Raspberry Pi 4, generating a quantum combinatorial optimization algorithm that saves the distance travelled and the batch of orders to be made. In case of computational need, the robot will be able to parallelize part of the operations in hybrid computing (quantum + classical), accessing CPUs and QPUs distributed in a public or private cloud. We developed a stable environment (ARM64) inside the robot (Raspberry) to run gradient operations and other quantum algorithms on IBMQ, Amazon Braket (D-Wave), and Pennylane locally or remotely. The proof of concept, when run in the above stated quantum environments, showed the execution time of our algorithm with different public access simulators on the market, computational results of our picking and batching algorithm, and analyze the quantum real-time execution. Our findings are that the behavior of the Amazon Braket D-Wave is better than Gate-based Quantum Computing over 20 qubits, and that AWS-Braket has better time performance than Qiskit or Pennylane. Full article
(This article belongs to the Special Issue Quantum Optimization and Machine Learning)
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11 pages, 5368 KiB  
Article
Using Machine Learning for Quantum Annealing Accuracy Prediction
by Aaron Barbosa, Elijah Pelofske, Georg Hahn and Hristo N. Djidjev
Algorithms 2021, 14(6), 187; https://doi.org/10.3390/a14060187 - 21 Jun 2021
Cited by 6 | Viewed by 2179
Abstract
Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem [...] Read more.
Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters, such as the D-Wave’s chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem will be solvable to optimality with the D-Wave 2000Q. We extend these results by training a machine learning regression model that predicts the clique size found by D-Wave. Full article
(This article belongs to the Special Issue Quantum Optimization and Machine Learning)
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