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Physica Scripta

A cross-platform study of near-term quantum optimisation algorithms on the graphene defect problem

Kieran McDowall, Theodoros Kapourniotis, Christopher Oliver, Phalgun Lolur, Κωνσταντίνος Γεωργόπουλος

Published Aug 28, 2026• 0 citations
Publisher

Abstract

Abstract Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present a focussed, application-level hardware case study of near-term quantum optimisation algorithms applied to a dense quadratic unconstrained binary optimisation (QUBO) materials science problem. To solve this problem, we implement two methods, the variational quantum eigensolver and quantum annealing (QA), on commercially-available gate-based and QA devices that are accessible via Quantum-Computing-as-a-Service (QCaaS) models. To analyse the performance of these algorithms on our chosen problem, we use a toolbox of relevant metrics and compare performance against three classical algorithms. We employ quantum methods to solve our fully-connected QUBO of up to 72 variables, and find that algorithm performance beyond this is restricted by device connectivity, noise and classical computation time overheads. The classical method—simulated annealing—demonstrates the best performance, exhibiting polynomial scaling on the tested problem sizes.

DOI
10.1088/1402-4896/aea063

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Abstract Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present a focussed, application-level hardware case study of near-term quantum optimisation algorithms applied to a dense quadratic unconstrained binary optimisation (QUBO) materials science problem. To solve this problem, we implement two methods, the variational quantum eigensolver and quantum annealing (QA), on commercially-available gate-based and QA devices that are accessible via Quantum-Computing-as-a-Service (QCaaS) models. To analyse the performance of these algorithms on our chosen problem, we use a toolbox of relevant metrics and compare performance against three classical algorithms. We employ quantum methods to solve our fully-connected QUBO of up to 72 variables, and find that algorithm performance beyond this is restricted by device connectivity, noise and classical computation time overheads. The classical method—simulated annealing—demonstrates the best performance, exhibiting polynomial scaling on the tested problem sizes.
Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum optimisation algorithms using a dense Quadratic Unconstrained Binary Optimisation (QUBO) materials science problem as a representative test-case. To solve this problem, we implement two methods, the Variational Quantum Eigensolver (VQE) and Quantum Annealing (QA), on commercially-available gate-based and quantum annealing devices that are accessible via Quantum-Computing-as-a-Service (QCaaS) models. To analyse the performance of these algorithms, we use a toolbox of relevant metrics and compare performance against three classical algorithms. We employ quantum methods to solve fully-connected QUBOs of up to 727272 variables, and find that algorithm performance beyond this is restricted by device connectivity, noise and classical computation time overheads. The applicability of our approach goes beyond the selected configurational analysis test-case, and we anticipate that our approach will be of use for optimisation problems in general.
Quantum computers are expected to offer advantages in solving optimization problems challenging for classical computers. Quadratic Unconstrained Binary Optimization (QUBO) problems represent an important class of problems with relevance in finance and logistics. The Quantum Approximate Optimization Algorithm (QAOA) is a prominent candidate for solving QUBO problems on near-term quantum devices. In this paper, we evaluate the performance of both the standard QAOA and the adaptive derivative assembled problem tailored QAOA (ADAPT-QAOA) to solve QUBO problems of varying sizes and hardnesses for financial feature selection problems. Our main observation is that ADAPT-QAOA achieves substantially higher approximation ratios than standard QAOA for harder feature-selection problems (α = 0.6) with statistically significant improvements observed for problem sizes n = 6 and 14. However, the standard QAOA remains competitive for simpler problems. Additionally, we evaluate the practical feasibility and limitations of QAOA through a hardware-aware scaling analysis based on the real-device calibration data for various hardware platforms. We estimate that standard QAOA implementation on superconducting quantum computers provides a shorter time-to-solution compared to trapped-ion devices, while trapped-ion devices yield more favorable error rates. Our findings provide a comprehensive overview of the challenges, trade-offs, and strategies for deploying QAOA-based methods on near-term quantum hardware.
Quantum computing is an important developing technology with the potential to revolutionise the landscape of scientific and business problems that can be practically addressed. The widespread excitement derives from the potential for a fault tolerant quantum computer to solve previously intractable problems. Such a machine is not expected to be available until 2030 at least. Thus we are currently in the so-called NISQ era where more heuristic quantum approaches are being applied to early versions of quantum hardware. In this paper we seek to provide a more accessible explanation of many of the more technical aspects of quantum computing in the current NISQ era exploring the 2 main hybrid classical-quantum algorithms, QAOA and VQE, as well as quantum annealing. We apply these methods, to an example of combinatorial optimisation in the form of a facilities location problem. Methods explored include the applications of different types of mixer (X, XY and a novel 3XY mixer) within QAOA as well as the effects of many settings for important meta parameters, which are often not focused on in research papers. Similarly, we explore alternative parameter settings in the context of quantum annealing. Our research confirms the broad consensus that quantum gate hardware will need to be much more capable than is available currently in terms of scale and fidelity to be able to address such problems at a commercially valuable level. Quantum annealing is closer to offering quantum advantage but will also need to achieve a significant step up in scale and connectivity to address optimisation problems where classical solutions are sub-optimal.
One of the potential use cases of a quantum computer is to solve combinatorial optimisation problems more efficiently than is possible with the most advanced classical computers. Combinatorial optimisation problems that appear in industry often involve a large number of constraints. This thesis investigates algorithmic techniques that improve the performance of quantum optimisation algorithms in solving problems with constraints. We test these techniques on customer data science problems. We study an alternative penalty method for encoding constraints in Ising Hamiltonians, which can be applied to various quantum algorithms. This method only introduces linear terms to the Ising Hamiltonian, allowing for more efficient use of hardware resources than the standard quadratic penalty method. These efficiency improvements are particularly beneficial for near-term devices with a limited number of qubits that are sparsely connected. We analyse the impact of using this alternative encoding method on the performance of the quantum approximate optimisation algorithm and quantum annealing applied to example problems in customer data science. Our results are based on numerical simulations and experiments on quantum hardware. We introduce a new variant of the quantum approximate optimisation algorithm that improves its ability to solve problems with constraints. In this variant of the algorithm, the strengths of penalty functions are associated with additional variational parameters, allowing them to take different values in each layer of the quantum circuit. We perform numerical simulations of multiple variants of the quantum approximate optimisation algorithm and compare their performance.
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of qubits and their connectivity, the QA hardware did not show such an advantage over classical methods in past benchmarking studies. Recent advancements in QA with more than 5000 qubits, enhanced qubit connectivity, and the hybrid architecture promise to realize the quantum advantage. Here, we use a quantum annealer with state-of-the-art techniques and benchmark its performance against classical solvers. To compare their performance, we solve over 50 optimization problem instances represented by large and dense Hamiltonian matrices using quantum and classical solvers. The results demonstrate that a state-of-the-art quantum solver has higher accuracy (~0.013%) and a significantly faster problem-solving time (~6561×) than the best classical solver. Our results highlight the advantages of leveraging QA over classical counterparts, particularly in hybrid configurations, for achieving high accuracy and substantially reduced problem solving time in large-scale real-world optimization problems.
Abstract Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where quantum computing has potential is in the speed-up of NP -hard optimisation problems that are common in industrial areas such as logistics and finance. Newcomers to the field of quantum computing who are interested in using this technology to solve optimisation problems do not have an easily accessible source of information on the current capabilities of quantum computers and algorithms. This paper aims to provide a comprehensive overview of the theory of quantum optimisation techniques and their practical application, focusing on their near-term potential for noisy intermediate scale quantum devices. The paper starts by drawing parallels between classical and quantum optimisation problems, highlighting their conceptual similarities and differences. Two main paradigms for quantum hardware are then discussed: analogue and gate-based quantum computers. While analog devices such as quantum annealers are effective for some optimisation problems, they have limitations and cannot be used for universal quantum computation. In contrast, gate-based quantum computers offer the potential for universal quantum computation, but they face challenges with hardware limitations and accurate gate implementation. The paper provides a detailed mathematical discussion with references to key works in the field, as well as a more practical discussion with relevant examples. The most popular techniques for quantum optimisation on gate-based quantum computers, the quantum approximate optimisation algorithm and the quantum alternating operator ansatz framework, are discussed in detail. However, it is still unclear whether these techniques will yield quantum advantage, even with advancements in hardware and noise reduction. The paper concludes with a discussion of the challenges facing quantum optimisation techniques and the need for further research and development to identify new, effective methods for achieving quantum advantage.