Speaker
Description
Portfolio optimization (PO) aims to find asset weights that balance risk and return, but the number of candidate portfolios grows exponentially with asset count, making exhaustive search intractable for classical methods such as mean-variance optimization, Monte Carlo simulation, and linear/quadratic programming. Quantum computing offers a potential path forward—superposition and entanglement allow many portfolio configurations to be explored simultaneously. Variational quantum algorithms (VQAs) such as VQE and QAOA are natural candidates for this task, but they suffer from well-documented trainability issues — local minima and barren plateaus that worsen with circuit depth and qubit count — limiting their practical use at realistic portfolio sizes. Patti et al.(2022) showed that MCMC-based optimizers can give VQAs provable convergence to the global minimum on toy combinatorial problems. Building on this result, we propose a VQA whose parameterized quantum circuit (PQC) is derived from the approximation of Imaginary Time Evolution (ITE) and trained using a gradient-guided MCMC optimizer (GradMCMC), which steers parameter updates along the descent direction while preserving MCMC's global-convergence guarantees. We apply this hybrid approach to a real-world portfolio optimization problem, reduced to eight strategies encoded across individual qubits, aiming to overcome the trainability barriers that have limited VQAs in financial applications. We present convergence plots benchmarking GradMCMC against standard optimizers, demonstrating faster convergence, and additionally study the effect of key optimizer hyperparameters on optimizer performance. Our results suggest that combining ITE-derived circuit structure with MCMC-guided training offers a promising route toward trainable, near-term quantum algorithms for combinatorial optimization problems beyond PO.
| Topic | Hybrid quantum-classical approaches for learning and optimization |
|---|---|
| Additional Topic | Quantum variational circuits and their applications |