QAOA Applications in Finance

Osama M. Raisuddin, Suvranu De

Choi Jaeho, Joongheon Kim

Rajavardhan Kashapogu, Saima Hasib, Akhtar Rasool

Quantum Approximate Optimization Algorithm (QAOA) is the notable advancement in quantum computing, which allows us to solve optimization problems differently. In this paper, we provide a detailed investigation of the possible applications of QAOA accompanied by an overview of previous implementations. This is where QAOA shines and can spin out solutions where ordinary methods takes millennia to converge with acceptable results for NP-hard optimization problems that involve transfer of $\mathbf{n}$ qubits between a quantum state. We present a comprehensive literature review in this paper, and potential areas of application where QAOA could be successfully used such as logistics, finance and Artificial Intelligence.

Yajie Hao, Qiming Ding, Xiao Yuan +1 more

Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales. The Quantum Approximate Optimization Algorithm (QAOA) offers a promising quantum framework, but conventional penalty-based formulations distort optimization landscapes and demand deep circuits, undermining scalability on near-term hardware. In this work, we introduce Hamming Weight Operators, a new class of constraint-aware operators that confine quantum evolution strictly within the feasible subspace. Building on this idea, we develop Adaptive Hamming Weight Operator QAOA, which dynamically selects the most effective operators to construct shallow, problem-tailored circuits. We validate our approach on benchmark tasks from both finance and high-energy physics, specifically portfolio optimization and two-jet clustering with energy balance. Across these problems, our method inherently satisfies all constraints by construction, converges faster, and achieves higher Approximation Ratios than penalty-based QAOA, while requiring roughly half as many gates. By embedding constraint-aware operators into an adaptive variational framework, our approach establishes a scalable and hardware-efficient pathway for solving practical constrained optimization problems on near-term quantum devices.

Mikita Vostry

Monsur Bolaji Olowoyo, 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.