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Algorithms
Special Issues
Quantum Optimization Theory, Algorithms, and Applications
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Quantum Optimization Theory, Algorithms, and Applications

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

Deadline for manuscript submissions: closed (31 December 2018) | Viewed by 26232

Special Issue Editor

Prof. Dr. Theodore B. Trafalis

E-Mail Website
Guest 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 with 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

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum computing
  • Optimization
  • Machine Learning

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Published Papers (2 papers)

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Research

24 pages, 2210 KiB  
Article
Embedding Equality Constraints of Optimization Problems into a Quantum Annealer
by Tomas Vyskocil and Hristo Djidjev
Algorithms 2019, 12(4), 77; https://doi.org/10.3390/a12040077 - 17 Apr 2019
Cited by 16 | Viewed by 5723
Abstract
Quantum annealers such as D-Wave machines are designed to propose solutions for quadratic unconstrained binary optimization (QUBO) problems by mapping them onto the quantum processing unit, which tries to find a solution by measuring the parameters of a minimum-energy state of the quantum [...] Read more.
Quantum annealers such as D-Wave machines are designed to propose solutions for quadratic unconstrained binary optimization (QUBO) problems by mapping them onto the quantum processing unit, which tries to find a solution by measuring the parameters of a minimum-energy state of the quantum system. While many NP-hard problems can be easily formulated as binary quadratic optimization problems, such formulations almost always contain one or more constraints, which are not allowed in a QUBO. Embedding such constraints as quadratic penalties is the standard approach for addressing this issue, but it has drawbacks such as the introduction of large coefficients and using too many additional qubits. In this paper, we propose an alternative approach for implementing constraints based on a combinatorial design and solving mixed-integer linear programming (MILP) problems in order to find better embeddings of constraints of the type ∑ x i = k for binary variables x i. Our approach is scalable to any number of variables and uses a linear number of ancillary variables for a fixed k. Full article
(This article belongs to the Special Issue Quantum Optimization Theory, Algorithms, and Applications)
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45 pages, 601 KiB  
Article
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
by Stuart Hadfield, Zhihui Wang, Bryan O’Gorman, Eleanor G. Rieffel, Davide Venturelli and Rupak Biswas
Algorithms 2019, 12(2), 34; https://doi.org/10.3390/a12020034 - 12 Feb 2019
Cited by 427 | Viewed by 18798
Abstract
The next few years will be exciting as prototype universal quantum processors emerge, enabling the implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation and which have the potential to [...] Read more.
The next few years will be exciting as prototype universal quantum processors emerge, enabling the implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation and which have the potential to significantly expand the breadth of applications for which quantum computers have an established advantage. A leading candidate is Farhi et al.’s quantum approximate optimization algorithm, which alternates between applying a cost function based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach, in the spirit of the quantum approximate optimization algorithm, to a wide variety of approximate optimization, exact optimization, and sampling problems. In addition to introducing the quantum alternating operator ansatz, we lay out design criteria for mixing operators, detail mappings for eight problems, and provide a compendium with brief descriptions of mappings for a diverse array of problems. Full article
(This article belongs to the Special Issue Quantum Optimization Theory, Algorithms, and Applications)
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