Quantum Approximate Optimisation Algorithm for Shari-ah-Constrained Portfolio Selection: A QUBO Formulation with Islamic Finance Penalty Terms
Abstract
Monsur Olowoyo and Wahab Abiona
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.
