This paper presents an application of the Quantum Approximate Optimisation Algorithm (QAOA) to Islamic portfolio optimisation, formulating the Shariah-constrained asset allocation problem as a Quadratic Unconstrained Binary Optimisation (QUBO) with explicit Islamic finance penalty terms. When augmented with AAOIFI Standard 21 constraints and IFSB capital adequacy guidelines, the portfolio allocation problem becomes NP-hard for large portfolios. Encoding these constraints as penalty terms in the QUBO Hamiltonian, the rare formulation in any domain incorporating religious law constraints, with penalty weights λShariah = 5.0 and λbudget = 2.0. Simulated on IBM Qiskit with a p=2 variational circuit using a high-fidelity synthetic dataset, the model demonstrates a simulated 55× speedup over classical enumeration on a 20-asset Shariah-constrained allocation problem. Quantum amplitude estimation further provides O(1/ε) speedup over classical Monte Carlo O(1/ε2 ) for Islamic portfolio risk estimation. The Shariah-adjusted sukuk-equity correlation (ρ = 0.18) is embedded in the quantum objective function.
This paper presents an application of the Quantum Approximate Optimisation Algorithm (QAOA) to Islamic portfolio optimisation, formulating the Shariah-constrained asset allocation problem as a Quadratic Unconstrained Binary Optimisation (QUBO) with explicit Islamic finance penalty terms. When augmented with AAOIFI Standard 21 constraints and IFSB capital adequacy guidelines, the portfolio allocation problem becomes NP-hard for large portfolios. Encoding these constraints as penalty terms in the QUBO Hamiltonian, the rare formulation in any domain incorporating religious law constraints, with penalty weights λShariah = 5.0 and λbudget = 2.0. Simulated on IBM Qiskit with a p=2 variational circuit using a high-fidelity synthetic dataset, the model demonstrates a simulated 55× speedup over classical enumeration on a 20-asset Shariah-constrained allocation problem. Quantum amplitude estimation further provides O(1/ε) speedup over classical Monte Carlo O(1/ε2 ) for Islamic portfolio risk estimation. The Shariah-adjusted sukuk-equity correlation (ρ = 0.18) is embedded in the quantum objective function.
This study explores the integration of quantum computing techniques, specifically the Quantum Approximate Optimization Algorithm (QAOA), with classical portfolio optimization frameworks through the Quadratic Unconstrained Binary Optimization (QUBO) approach. Using monthly turnover data from the National Stock Exchange of India (NSE), this paper demonstrates the construction of a QUBO matrix by encoding expected returns and covariance-based risk profiles. Binary asset inclusion constraints are introduced into portfolios and then optimised using both brute force enumeration and quantum inspired solvers. The analysis reveals those combinations including Index Futures and Index Options exhibit superior risk-adjusted performance (Sharpe Ratio≈0.286). The hybrid approach suggests the promise of quantum inspired models as means to improve financial decision making under uncertainty. The results also give a robust template for scalable asset selection models that operate within the constraints of quantum computing infrastructure.
Portfolio optimization, a core combinatorial optimization problem in quantitative finance, requires balancing return maximization and risk minimization within discrete asset sets. Classical algorithms often struggle with scalability and local optima traps when handling large-scale asset pools, limiting their practicality in dynamic markets. This study proposes a complete Quantum Approximate Optimization Algorithm (QAOA) workflow for portfolio optimization, from problem formalization to experimental validation. We first transform the portfolio optimization problem into a Quadratic Unconstrained Binary Optimization (QUBO) framework, then design a parameterized QAOA circuit with adjustable layers to balance expressiveness and noise resilience. We propose a methodology using Qiskit for quantum simulation and classical optimizers for parameter tuning, we propose implementing the algorithm on real-world S&P 500 stock data. We could also analyze the impact of quantum hardware noise and propose mitigation strategies, providing actionable insights for Noisy intermediate-scale quantum computing (NISQ)-era implementations. This work bridges quantum algorithm design with real-world financial applications, offering a theoretical framework for quantum-driven portfolio optimization.
Large-scale portfolio optimization is hard because investors must balance risk, return, diversification, and liquidity across many assets with complex constraints. Classical methods, such as quadratic programming or metaheuristics, often become slow or less effective as the number of assets and factors grows. In this project, I explore the use of the Quantum Approximate Optimization Algorithm (QAOA) as a hybrid quantum–classical approach to portfolio selection. The framework encodes portfolio decisions as qubits and represents financial objectives—such as mean–variance trade-offs or risk-adjusted return—inside a parameterized quantum circuit. Classical optimization is then used to tune the circuit parameters so that the quantum system converges toward low-risk, high-return portfolios. Multi-factor constraints, including sector limits, liquidity rules, ESG scores, and macroeconomic risk factors, are integrated into the Hamiltonian as penalty terms. A qualitative comparison with classical solvers (e.g., mixed-integer programming and simulated annealing) suggests that QAOA can scale more gracefully in high-dimensional settings and handle complex constraint structures. Overall, the project shows how quantum hybrid optimization could support future portfolio management, linking theoretical quantum algorithms with practical, sustainability-aware investment strategies.
Quantum finance represents a pivotal and cutting-edge application domain within the burgeoning field of quantum computing. In this work, we propose a two-step quantum approximate optimization algorithm (two-step QAOA) for portfolio optimization and risk assessment. The algorithm initiates by formulating the stock selection problem as a quadratic unconstrained binary optimization (QUBO) problem and employs a classical-quantum hybrid method to find the ground state of the Hamiltonian. We then introduce an energy-based characteristic indicator U∈[0,1), which quantitatively evaluates portfolio performance under customizable investment preferences, effectively capturing the trade-off between expected return and risk. The number of qubits required scales with the number of stocks N in the pool, and the number of Hamiltonian terms is O(N2). Numerical simulations show that the algorithm provides consistent and reasonable assessment results on both training and test datasets under different investment preferences (aggressive or conservative), validating the capability of the characteristic indicator to extract intrinsic information from the portfolios. Additionally, by incorporating warm-starting and digitized counterdiabatic techniques, the algorithm achieves improved scalability and faster convergence. Our work presents a flexible and practical algorithmic framework for applying quantum computing in the financial domain.
We present QAMOO, a novel quantum computing framework for multi-objective portfolio optimization that simultaneously optimizes four distinct financial objectives—expected return, portfolio volatility, transaction costs, and entropy-based diversification—within a unified quantum Hamiltonian formulation. Unlike prior quantum finance approaches that treat diversification as a post-hoc penalty or encode transaction fees as scalarized weights, QAMOO embeds a Shannon entropy term directly into the quantum cost function through amplitude encoding of the portfolio weight vector. This formulation enables joint optimization over a non-convex objective landscape that cannot be faithfully reduced to a classical convex program without exponential complexity growth. The framework employs the Quantum Approximate Optimization Algorithm (QAOA) with pre-trained parameter transfer, executed on IBM Quantum hardware featuring heavy-hex topology processors with up to 156 qubits. A custom Pareto engine discovers the complete frontier of non-dominated portfolio solutions, enabling investors to select allocations matching their individual risk preferences. Empirical evaluation on a multi-asset portfolio demonstrates a 0.21% hypervolume improvement over the state-of-the-art classical multi-objective evolutionary algorithm (NSGA-III), while requiring approximately 30% fewer optimization cycles. The quantum-derived portfolios exhibit 23% lower turnover-adjusted volatility after accounting for realistic transaction fees. QAMOO establishes a new research direction at the intersection of quantum computing and quantitative finance, providing a hardware-aware optimization paradigm that integrates entropy-driven diversification directly into quantum annealing and gate-model formulations.
Financial modeling and risk analysis involve computationally intensive tasks -- Monte Carlo simulation for derivative pricing, portfolio optimisation over high-dimensional asset spaces, and Value-at-Risk estimation from complex multivariate distributions -- where quantum computing offers potential polynomial-to-quadratic speedups. This paper proposes the Quantum Financial Computation Framework (QFCF), a systematic evaluation of quantum algorithms for four core financial computing tasks: option pricing (quantum amplitude estimation for Monte Carlo), portfolio optimisation (QAOA and VQE on quadratic unconstrained binary optimisation formulations), credit risk assessment (quantum Bayesian inference), and Value-at-Risk estimation (quantum arithmetic circuits). QFCF is evaluated on 16 financial benchmark problems spanning European and Asian option pricing, 50-500 asset portfolio optimisation, and credit portfolio loss distributions on near-term (NISQ) and fault-tolerant quantum hardware models. Key results: quantum amplitude estimation achieves quadratic speedup over classical Monte Carlo for option pricing with circuit depth scaling as O(1/ε) versus classical O(1/ε2); QAOA achieves portfolio optimisation solution quality within 4.8% of classical branch-and-bound for 50-asset problems; quantum Bayesian credit scoring reduces inference time by 38x for 200-variable credit networks. The framework introduces the Quantum Financial Utility Index (QFUI) and quantitative quantum advantage thresholds for each financial task.