Quantum computing offers new possibilities for solving combinatorial optimization problems with rapidly growing search spaces. Among emerging hardware platforms, photonic quantum computers based on boson sampling provide a promising approach for sampling-based optimization methods. In this work, we investigate the application of the Binary Bosonic Solver, a hybrid quantum-classical algorithm designed for photonic quantum processors, to the binary portfolio optimization problem derived from the classical mean-variance framework. In addition to evaluating the feasibility of solving such problems on photonic quantum hardware, we analyze the behavior of the Binary Bosonic Solver algorithm under different architectural and optimization parameters, including interferometer loop configurations and gradient estimation methods. Benchmark instances are generated using historical financial market data, and experiments are performed both on a photonic quantum computer simulator and on the ORCA PT-1 photonic quantum processor installed at Poznan Supercomputing and Networking Center, with results compared to those obtained using a classical optimization algorithm. The results demonstrate that portfolio optimization can be successfully executed on current photonic quantum hardware and that the Binary Bosonic Solver algorithm consistently produces feasible and high-quality solutions, highlighting the practical potential of photonic quantum computing for combinatorial optimization problems.
Quantum computing offers new possibilities for solving combinatorial optimization problems with rapidly growing search spaces. Among emerging hardware platforms, photonic quantum computers based on boson sampling provide a promising approach for sampling-based optimization methods. In this work, we investigate the application of the Binary Bosonic Solver, a hybrid quantum-classical algorithm designed for photonic quantum processors, to the binary portfolio optimization problem derived from the classical mean-variance framework. In addition to evaluating the feasibility of solving such problems on photonic quantum hardware, we analyze the behavior of the Binary Bosonic Solver algorithm under different architectural and optimization parameters, including interferometer loop configurations and gradient estimation methods. Benchmark instances are generated using historical financial market data, and experiments are performed both on a photonic quantum computer simulator and on the ORCA PT-1 photonic quantum processor installed at Poznan Supercomputing and Networking Center, with results compared to those obtained using a classical optimization algorithm. The results demonstrate that portfolio optimization can be successfully executed on current photonic quantum hardware and that the Binary Bosonic Solver algorithm consistently produces feasible and high-quality solutions, highlighting the practical potential of photonic quantum computing for combinatorial optimization problems.
Binary optimisation tasks are ubiquitous in areas ranging from logistics to cryptography. The exponential complexity of such problems means that the performance of traditional computational methods decreases rapidly with increasing problem sizes. Here, we propose a new algorithm for binary optimisation, the Bosonic Binary Solver, designed for near-term photonic quantum processors. This variational algorithm uses samples from a quantum optical circuit, which are post-processed using trainable classical bit-flip probabilities, to propose candidate solutions. A gradient-based training loop finds progressively better solutions until convergence. We perform ablation tests that validate the structure of the algorithm. We then evaluate its performance on an illustrative range of binary optimisation problems, using both simulators and real hardware, and perform comparisons to classical algorithms. We find that this algorithm produces high-quality solutions to these problems. As such, this algorithm is a promising method for leveraging the scalable nature of photonic quantum processors to solve large-scale real-world optimisation problems.
Quantum computers are increasingly being integrated into classical computing environments, particularly within supercomputing and data centers, where they serve as accelerators for solving a wide range of specific problems. Previous research has indicated that quantum computers have the potential to resolve optimization problems with theoretically lower computational complexity than classical algorithms. However, in practical scenarios, even minor instances of these problems often require substantial computational resources, enhanced quality quantum hardware, and the results may not always be optimal. In this paper, we highlight the importance of hybrid systems, combining quantum and classical computations to address growing problem sizes and computational demands. We focus on optimization problems using hardware and software-enhanced quantum computers operational within a novel quantum–classical hybrid setup, incorporating GPUs and photonic quantum computers. The study specifically addresses combinatorial optimization problems, such as the Max-Cut and the Job Shop Scheduling Problem, in addition to selected machine learning classification use cases. Notably, the quantum algorithm in Max-Cut optimization outperformed complete solution searches, especially for larger problem instances. For the Job-Shop Scheduling Problem, we made a significant advancement by successfully solving substantially larger instances compared to our previous previous work. Furthermore, selected hybrid neural networks incorporating quantum layers showed improved stability, though without a clear quality advantage over classical models. The paper also highlights the rapid progress and technological achievements in both hardware and software used in near-term photonic quantum computers, suggesting a promising future for quantum–classical hybrid systems in useful applications.
Quantum annealing has emerged as a promising computational paradigm for solving large-scale combinatorial optimization problems that are intractable for classical algorithms. Financial portfolio optimization, which involves balancing expected returns against risk under multiple practical constraints, represents one of the most challenging optimization tasks in quantitative finance. Traditional approaches based on mean-variance theory, heuristic meta-optimization, and classical quadratic programming often struggle to scale efficiently as the dimensionality of assets and constraints increases. This study explores the application of quantum annealing techniques to financial portfolio optimization by formulating the problem as a quadratic unconstrained binary optimization model suitable for quantum hardware. The paper provides a systematic mapping of portfolio objectives and constraints into the Ising Hamiltonian framework and analyzes how quantum tunneling and probabilistic state transitions can enhance convergence toward near-global optima. Comparative insights between classical solvers and quantum annealing-based approaches are discussed in terms of solution quality, computational efficiency, and scalability. Furthermore, the study highlights current hardware limitations, embedding challenges, and noise effects that influence optimization performance. The findings indicate that quantum annealing offers substantial potential for accelerating portfolio optimization in high-dimensional financial systems, particularly in scenarios involving complex constraints and dynamic market conditions, thereby establishing a foundation for future quantum-driven financial decision-support systems.
Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration into alternative paradigms such as quantum computing. In this paper, we investigate the application of photonic quantum computing to solve combinatorial optimization problems. Leveraging the principles of quantum mechanics, we demonstrate how photonic quantum computers can efficiently explore solution spaces and identify optimal solutions for a range of combinatorial problems. We provide an overview of quantum algorithms tailored for combinatorial optimization for different quantum architectures (boson sampling, quantum annealing and gate-based quantum computing). Additionally, we discuss the advantages and challenges of implementing those algorithms on photonic quantum hardware. Through experiments run on an 8-qumode photonic quantum device, as well as numerical simulations, we evaluate the performance of photonic quantum computers in solving representative combinatorial optimization problems, such as the Max-Cut problem and the Job Shop Scheduling Problem.
Portfolio optimization under conditions of risk and market uncertainty remains a foundational challenge in financial economics and investment management. Classical optimization frameworks, including mean–variance models and stochastic programming approaches, often struggle with high-dimensional asset universes, nonlinear correlations, and dynamic market regimes. This paper examines quantum computing approaches to portfolio optimization under risk and market uncertainty, focusing on hybrid quantum–classical algorithms designed to enhance combinatorial optimization and probabilistic modeling. By integrating quantum annealing, variational quantum circuits, and quantum-enhanced sampling techniques with classical financial analytics, the study evaluates their potential to improve computational efficiency and scenario sensitivity. The analysis considers both theoretical advantages and practical limitations within the Noisy Intermediate-Scale Quantum (NISQ) era. The findings suggest that quantum-assisted optimization may complement traditional portfolio models by expanding feasible solution spaces and improving robustness under uncertainty, thereby contributing to more adaptive and resilient investment strategies.
In finance, portfolio optimization aims at finding optimal investments maximizing a trade-off between return and risks, given some constraints. Classical formulations of this quadratic optimization problem have exact or heuristic solutions, but the complexity scales up as the market dimension increases. Recently, researchers are evaluating the possibility of facing the complexity scaling issue by employing quantum computing. In this paper, the problem is solved using the Variational Quantum Eigensolver (VQE), which in principle is very efficient. The main outcome of this work consists of the definition of the best hyperparameters to set, in order to perform Portfolio Optimization by VQE on real quantum computers. In particular, a quite general formulation of the constrained quadratic problem is considered, which is translated into Quadratic Unconstrained Binary Optimization by the binary encoding of variables and by including constraints in the objective function. This is converted into a set of quantum operators (Ising Hamiltonian), whose minimum eigenvalue is found by VQE and corresponds to the optimal solution. In this work, different hyperparameters of the procedure are analyzed, including different ansatzes and optimization methods by means of experiments on both simulators and real quantum computers. Experiments show that there is a strong dependence of solutions quality on the sufficiently sized quantum computer and correct hyperparameters, and with the best choices, the quantum algorithm run on real quantum devices reaches solutions very close to the exact one, with a strong convergence rate towards the classical solution, even without error-mitigation techniques. Moreover, results obtained on different real quantum devices, for a small-sized example, show the relation between the quality of the solution and the dimension of the quantum processor. Evidences allow concluding which are the best ways to solve real Portfolio Optimization problems by VQE on quantum devices, and confirm the possibility to solve them with higher efficiency, with respect to existing methods, as soon as the size of quantum hardware will be sufficiently high.