Variational Quantum Algorithms for Portfolio Optimization: Benchmarking QAOA and VQE Against Classical Solvers on Near-Term Quantum Hardware
Variational quantum algorithms -- particularly the Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE) -- have been widely proposed as near-term candidates for achieving quantum advantage in combinatorial optimization problems relevant to finance, including portfolio optimization, risk parity, and credit risk assessment. However, realistic benchmarking of these algorithms on current quantum hardware against state-of-the-art classical solvers has been limited by hardware access constraints and lack of standardized evaluation methodologies. This paper presents the most comprehensive empirical benchmarking study of QAOA and VQE for financial portfolio optimization to date, executing experiments on IBM Quantum Eagle (127-qubit), IBM Quantum Osprey (433-qubit), and IonQ Aria (25-qubit) processors across portfolio sizes from 10 to 50 assets, and comparing solution quality and runtime against Gurobi, D-Wave Advantage (quantum annealing), and simulated annealing baselines. Current QAOA implementations at p=3 circuit depth achieve mean solution quality 18.4% below Gurobi on 30-asset portfolios, with hardware noise as the dominant limiting factor. D-Wave Advantage outperforms gate-model QAOA for portfolio sizes below 40 assets on current hardware. We introduce a Quantum Finance Readiness Index (QFRI) that maps algorithm performance trajectories against projected hardware improvement curves, estimating practical quantum advantage emergence for 100-asset portfolios at approximately 2028-2031 under optimistic noise reduction scenarios. This work provides financial institutions with an honest evidence base for quantum computing investment planning.
