We introduce novel algorithms for solving dynamic programming problems in economics on a quantum annealer, a specialized quantum computer used for combinatorial optimization. Quantum annealers begin in a superposition of all states and generate candidate global solutions in milliseconds, regardless of problem size. In contrast to existing methods, those developed in this paper (1) recover value and policy functions, (2) avoid fundamental scaling bottlenecks, and (3) are already implementable for small (but non‐trivial) problems on current hardware. We demonstrate the method by solving the real business cycle model on a quantum annealer.
We introduce novel algorithms for solving dynamic programming problems in economics on a quantum annealer, a specialized quantum computer used for combinatorial optimization. Quantum annealers begin in a superposition of all states and generate candidate global solutions in milliseconds, regardless of problem size. In contrast to existing methods, those developed in this paper (1) recover value and policy functions, (2) avoid fundamental scaling bottlenecks, and (3) are already implementable for small (but non‐trivial) problems on current hardware. We demonstrate the method by solving the real business cycle model on a quantum annealer.
We introduce a novel approach to solving dynamic programming problems, such as those in many economic models, on a quantum annealer, a specialized device that performs combinatorial optimization. Quantum annealers attempt to solve an NP-hard problem by starting in a quantum superposition of all states and generating candidate global solutions in milliseconds, irrespective of problem size. Using existing quantum hardware, we achieve an order-of-magnitude speed-up in solving the real business cycle model over benchmarks in the literature. We also provide a detailed introduction to quantum annealing and discuss its potential use for more challenging economic problems.
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum computing, quantum annealing (QA), has been proposed to solve these problems by encoding optimization problems into physical energy landscapes and solving them by quantum tunnelling systematically through exploration of solution space. This is a critical review that summarizes the current applications of quantum annealing to combinatorial optimization and includes a theoretical background, hardware designs, algorithm implementation strategies, encoding and embedding schemes, protocols to benchmark quantum annealing, areas of implementation, and links with the quantum algorithms implementation with gate-based hardware and classical solvers. We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers (Chimera, Pegasus, Zephyr topologies), and emergent architectures (Lechner-Hauke-Zoller systems, Rydberg atom platforms), and hybrids of quantum and classical computation. Through our analysis, we find that overhead in embedding and encoding is the largest determinant of the scalability and performance (this is not just the number of qubits). Minor embeddings also usually have a physical qubit count per logical variable of between 5 and 12 qubits, which limits effective problem capacity by 80-92% and, due to chain-breaking errors, compromises the quality of solutions.
Abstract Quantum computing is increasingly discussed as a possible source of new computational methods for economics, but its relevance depends on whether economic bottlenecks match quantum algorithmic primitives. This critical review evaluates that match for computational economics. It synthesizes work on quantum amplitude estimation and quantum Monte Carlo for simulation and risk measurement; quadratic unconstrained binary optimization (QUBO), Ising formulations, quantum annealing, and the quantum approximate optimization algorithm for discrete optimization; and quantum linear-algebra and machine-learning primitives for econometrics and model solution. The review argues that there is no general-purpose quantum algorithm for economics analogous to Shor's algorithm for factoring. Credible claims are problem-class specific and depend on state preparation, output requirements, conditioning, hardware noise, embedding overhead, and comparison with strong classical and quantum-inspired baselines. The most mature economic applications are derivative pricing and financial risk, payment-system liquidity optimization, quantum Monte Carlo for stress testing, and early quantum-annealing formulations of dynamic programming. Transportation and infrastructure applications are relevant mainly as networked economic optimization problems. The article proposes an evidence ladder for quantum computational economics and a research agenda centered on reproducible benchmarks, economically meaningful objective functions, end-to-end resource accounting, and evaluation by economic value rather than hardware novelty. JEL Classification: C02; C15; C61; C63; C88; E37; G11; G17; R41
A combinatorial optimization problem (COP) is the problem of finding the optimal solution in a finite set. When the size of the feasible solution set is large, the complexity of the problem increases, and it is not easy to solve in a reasonable time with the current classical computer technology. Quantum annealing (QA) is a method that replaces classical simulated annealing (SA) methods that do not solve these cases. Therefore, several attempts have been made to solve this problem using a special-purpose quantum annealer to which the QA method is applied. In this survey, we analyze recent studies that solve real-scale COPs using quantum annealers. Through this, we discuss how to reduce the size of the COP to be input to overcome the hardware limitations of the existing quantum annealer. Additionally, we demonstrated the applicability of quantum annealer to COP on a practical scale by comparing and analyzing the results of the classical simulated annealing (SA) and QA method from each study.
Quantum computing has emerged as a promising computational paradigm with the potential to solve problems that are intractable for classical computers. This paper provides an overview of the current state of quantum computing, including its historical development, hardware advancements, applications, and challenges. Special attention is given to combinatorial optimization, which is considered one of the most promising application domains. The limitations of current quantum systems and future research directions are also discussed. This paper presents a comparative study between a conventional D-Wave-based simulated annealing approach and a proposed hybrid optimization model for solving largescale combinatorial optimization problems. The study focuses on benchmark problems, including AES, TSP gr24, and a real-world load balancing problem, all formulated as QUBO models. The D-Wave approach employs the dwave-neal simulated annealing engine with various parameter settings, while the proposed model introduces a decomposition-based framework combined with adaptive parameter control and iterative refinement. The experimental results demonstrate that the proposed model consistently outperforms the conventional approach in terms of solution quality, achieving significantly lower energy values across all problem instances. In particular, for the TSP gr24 problem, the proposed model achieves near-optimal solutions with substantially reduced computation time. For large-scale problems such as AES and load balancing, the proposed model maintains scalability and robustness, whereas the conventional approach suffers from increased computational cost and performance degradation. Although the proposed method introduces additional computational steps, its hybrid structure effectively mitigates limitations related to local minima, parameter sensitivity, and scalability. These findings indicate that integrating classical optimization techniques with quantum-inspired methods is essential for practical applications. The proposed model provides a promising framework for solving complex real-world optimization problems and highlights the importance of hybrid approaches in advancing quantum annealing technologies.
This paper investigates the application of quantum annealing for the combinatorial optimization challenges inherent in large-scale simulations. We demonstrate that classical algorithms frequently encounter significant computational bottlenecks when tackling complex problems such as molecular dynamics simulations, materials design, and financial modeling. Quantum annealing, leveraging quantum tunneling, offers a potential paradigm shift by providing a mechanism for directly mapping these optimization problems onto quantum hardware and exploring the solution space with enhanced efficiency. This work presents a theoretical framework outlining the approach and discusses the core principles underlying its implementation. The focus is on the potential to accelerate computationally intensive simulations, addressing a critical limitation in current simulation methodologies. We explore the challenges and opportunities associated with this emerging technology, emphasizing its role in overcoming the limitations of classical optimization techniques. The primary goal is to provide a foundational understanding of how quantum annealing can be strategically applied to significantly improve the speed and accuracy of large-scale simulations.