We present a hybrid classical-quantum framework for portfolio construction and rebalancing. Asset selection is performed using Ledoit-Wolf shrinkage covariance estimation combined with hierarchical correlation clustering to extract n = 10 decorrelated stocks from the S&P 500 universe without survivorship bias. Portfolio weights are optimised via an entropy-regularised Genetic Algorithm (GA) accelerated on GPU, alongside closed-form minimum-variance and equal-weight benchmarks. Our primary contribution is the formulation of the portfolio rebalancing schedule as a Quadratic Unconstrained Binary Optimisation (QUBO) problem. The resulting combinatorial optimisation task is solved using the Quantum Approximate Optimisation Algorithm (QAOA) within a walk-forward framework designed to eliminate lookahead bias. This approach recasts dynamic rebalancing as a structured binary scheduling problem amenable to variational quantum methods. Backtests on S&P 500 data (training: 2010-2024; out-of-sample test: 2025, n = 249 trading days) show that the GA + QAOA strategy attains a Sharpe ratio of 0.588 and total return of 10.1%, modestly outperforming the strongest classical baseline (GA with 10-day periodic rebalancing, Sharpe 0.575) while executing 8 rebalances versus 24, corresponding to a 44.5% reduction in transaction costs. Multi-restart QAOA (4096 measurement shots per run) exhibits concentrated probability mass on high-quality schedules, indicating stable convergence of the variational procedure. These findings suggest that hybrid classical-quantum architectures can reduce turnover in portfolio rebalancing while preserving competitive risk-adjusted performance, providing a structured testbed for near-term quantum optimisation in financial applications.
We present a hybrid classical-quantum framework for portfolio construction and rebalancing. Asset selection is performed using Ledoit-Wolf shrinkage covariance estimation combined with hierarchical correlation clustering to extract n = 10 decorrelated stocks from the S&P 500 universe without survivorship bias. Portfolio weights are optimised via an entropy-regularised Genetic Algorithm (GA) accelerated on GPU, alongside closed-form minimum-variance and equal-weight benchmarks. Our primary contribution is the formulation of the portfolio rebalancing schedule as a Quadratic Unconstrained Binary Optimisation (QUBO) problem. The resulting combinatorial optimisation task is solved using the Quantum Approximate Optimisation Algorithm (QAOA) within a walk-forward framework designed to eliminate lookahead bias. This approach recasts dynamic rebalancing as a structured binary scheduling problem amenable to variational quantum methods. Backtests on S&P 500 data (training: 2010-2024; out-of-sample test: 2025, n = 249 trading days) show that the GA + QAOA strategy attains a Sharpe ratio of 0.588 and total return of 10.1%, modestly outperforming the strongest classical baseline (GA with 10-day periodic rebalancing, Sharpe 0.575) while executing 8 rebalances versus 24, corresponding to a 44.5% reduction in transaction costs. Multi-restart QAOA (4096 measurement shots per run) exhibits concentrated probability mass on high-quality schedules, indicating stable convergence of the variational procedure. These findings suggest that hybrid classical-quantum architectures can reduce turnover in portfolio rebalancing while preserving competitive risk-adjusted performance, providing a structured testbed for near-term quantum optimisation in financial applications.
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.
This paper investigates and compares quantum and classical investment strategies for portfolio construction under realistic trading and allocation constraints. The study considers a multi-period portfolio re-balancing setting in which asset weights are subject to lower and upper bounds, class-level exposure restrictions, and turnover limitations. On the quantum side, the portfolio selection problem is reformulated as a quadratic unconstrained binary optimization (QUBO) model through a finite binary encoding of asset weights, and subsequently embedded into a constrained quadratic model (CQM) solved by a hybrid quantum-classical optimization workflow. On the classical side, benchmark allocation strategies are introduced to provide an economically meaningful reference for performance assessment. The proposed framework jointly evaluates portfolio efficiency from two complementary perspectives: business performance, measured through return, volatility, and a measure of the trade-off between them, the Sharpe ratio; and computational performance, assessed through solver structure, constraint handling, and hardware execution characteristics. The resulting comparison provides a rigorous basis for understanding the practical role of quantum annealing in constrained portfolio optimization, while clarifying both its modeling advantages and its current implementation limitations relative to established classical approaches.
We test whether quantum-inspired optimization, specifically Quadratic Unconstrained Binary Optimization (QUBO) solved via simulated annealing, can improve implementable portfolio performance compared to classical baselines when realistic frictions are included. Our experimental design uses daily returns from the Center for Research in Security Prices (CRSP) for S&P500 constituents spanning 2014–2025, with monthly rebalancing, explicit transaction costs, and turnover accounting. We compare QUBO portfolios against equal-weight and convex mean–variance portfolios across multiple universe sizes (20, 50, 67 assets), lookback windows, and transaction-cost levels. Statistical significance is assessed via paired moving-block bootstrap on out-of-sample net returns. A hyperparameter sweep over encoding depth, penalty coefficients, and turnover reveals 19 of 81 QUBO configurations beat the equal-weight baseline, with the best achieving a Sharpe of 1.59 versus 1.42. However, under a fair walk forward model-selection protocol that eliminates look-ahead bias, the QUBO strategy does not achieve statistically significant superiority over either classical benchmark (∆Sharpe vs. equal weight: −0.13, 95% CI [−0.46,0.16]; vs. mean–variance: −0.29, 95% CI [−0.63,0.06]). Excessive turnover (averaging ∼1.0 per rebalance) is identified as the primary bottleneck. We conclude that current QUBO formulations with simulated annealing do not yet deliver a robust, implementable edge over well-tuned convex optimizers, though the framework remains a promising research direction as quantum hardware and hybrid solvers mature.
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.
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.
Classical mean-variance optimization is powerful in theory but fragile in practice, often producing highly concentrated, high-turnover portfolios. Naive equal-weight (1/N) portfolios are more robust but largely ignore cross-sectional information. We propose a quantum stochastic walk (QSW) framework that embeds assets in a weighted graph and derives portfolio weights from the stationary distribution of a hybrid quantum-classical walk. The resulting allocations behave as a “smart 1/N” portfolio: structurally close to equal-weight, but with small, data-driven tilts and a controllable level of trading. On recent S&P 500 universes, QSW portfolios match the diversification and stability of 1/N while delivering higher risk-adjusted returns than both mean-variance and naive benchmarks. A comprehensive hyper-parameter grid search shows that this behavior is structural rather than the result of fine-tuning and yields simple design rules for practitioners. A 34-year, multi-universe robustness study with rolling re-optimization further demonstrates that the QSW optimizer preserves these advantages across market regimes. Overall, the QSW framework improves risk-adjusted performance while maintaining strong diversification and moderate turnover.