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Mathematics
Special Issues
Recent Advances in Quantum Optimization
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Recent Advances in Quantum Optimization

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 30 September 2026 | Viewed by 1646

Special Issue Editor

Dr. Pascal Halffmann

E-Mail Website
Guest Editor
Department of Financial Mathematics, Fraunhofer Institute for Industrial Mathematics ITWM, 67663 Kaiserslautern, Germany
Interests: optimization; multiobjective optimization; quantum computing; quantum optimization; financial mathematics

Special Issue Information

Dear Colleagues,

Quantum computing has rapidly emerged as one of the most exciting frontiers in modern science and technology, drawing attention across disciplines for its potential—especially in computationally demanding areas like optimization. Optimization problems lie at the heart of countless real-world applications, from logistics and finance to machine learning and energy systems with a constant need for more performant solution strategies. As pointed out in the seminal work “Challenges and opportunities in quantum optimization” by Abbas et al., quantum computing promises to offer a paradigm shift by potentially solving or approximating solutions to hard optimization problems more efficiently than classical counterparts. However, this new field of quantum optimization requires significant efforts in research towards a quantum advantage.

I am pleased to invite you to contribute to this Special Issue that provides a platform for original research that fills research gaps in quantum optimization. Specifically, the scope of this Special Issue covers the development of innovative quantum algorithms that tackle optimization problems, preferably problems stemming from application areas with more complex structures, uncertain data, or multiple objectives. Research areas may include (but are not limited to) the following: quantum optimization algorithms on gate-based quantum computers, hybrid algorithms using quantum annealing, quantum multiobjective optimization algorithms, quantum robust optimization algorithms, and the benchmarking of quantum optimization algorithms.

We look forward to receiving your contributions.

Dr. Pascal Halffmann
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 250 words) can be sent to the Editorial Office for assessment.

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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 optimization
  • optimization
  • operations research
  • quantum computing

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Published Papers (2 papers)

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Research

27 pages, 842 KB  
Article
An Automated Synthesis Framework for Benchmarking Quantum Resource Costs of Symmetric-Key Cryptography
by Chanho Choi, Jinseob Oh, SangMan Lee, Geumhwan Cho and Dooho Choi
Mathematics 2026, 14(4), 719; https://doi.org/10.3390/math14040719 - 19 Feb 2026
Viewed by 294
Abstract
Modern information security relies heavily on symmetric-key cryptography such as AES. As quantum computing advances, these classical schemes face increasing pressure from quantum key-search attacks, most notably Grover’s algorithm. To evaluate and compare quantum security quantitatively, the core components of symmetric-key algorithms must [...] Read more.
Modern information security relies heavily on symmetric-key cryptography such as AES. As quantum computing advances, these classical schemes face increasing pressure from quantum key-search attacks, most notably Grover’s algorithm. To evaluate and compare quantum security quantitatively, the core components of symmetric-key algorithms must be implemented and optimized as quantum circuits. Among them, the S-box is a key source of nonlinearity and often dominates the circuit cost. In this paper, we introduce ADOQ (Automatic Depth Optimizer for Quantum circuits), a modular Python (version 3.13.3) framework that automatically synthesizes reversible quantum circuits from S-box specifications and applies a sequence of depth optimization techniques to produce optimized QASM circuits. Our experiments show that ADOQ achieves circuit depths comparable to prior work on 4-qubit S-boxes, and it also supports synthesis for larger S-boxes. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Optimization)
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17 pages, 8459 KB  
Article
Efficient Ground State Energy Estimation of LiCoO2 Using the FMO-VQE Hybrid Quantum Algorithm
by Yoonho Choe, Doyeon Kim, Doha Kim and Younghun Kwon
Mathematics 2026, 14(1), 44; https://doi.org/10.3390/math14010044 - 22 Dec 2025
Viewed by 698
Abstract
The Variational Quantum Eigensolver (VQE) is a quantum algorithm for estimating ground-state energies, with promising applications in material science, drug discovery, and battery research. A key challenge is the limited number of qubits available on current quantum devices, which restricts the size of [...] Read more.
The Variational Quantum Eigensolver (VQE) is a quantum algorithm for estimating ground-state energies, with promising applications in material science, drug discovery, and battery research. A key challenge is the limited number of qubits available on current quantum devices, which restricts the size of molecular systems that can be studied. To address this limitation, we apply the Fragment Molecular Orbital (FMO) method in combination with VQE, referred to as FMO-VQE. This approach divides a system into smaller fragments, making the quantum calculations more tractable. While earlier studies demonstrated this method only for hydrogen clusters, we extend the application to lithium cobalt oxide, a widely used cathode material in lithium-ion batteries. Using FMO-VQE, we estimate the ground-state energy of this complex system while reducing the number of required qubits from 24 to 14, without significant loss of accuracy compared to classical methods. This reduction highlights the potential of FMO-VQE to overcome hardware limitations and make quantum simulations of larger molecules feasible. The results suggest a practical path for applying near-term quantum computers to real-world challenges, opening opportunities for advancements in the battery industry and drug design. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Optimization)
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