Abstract Recent research on quantum walk-based optimization has shown theoretical potential as an alternative to variational algorithms, avoiding local minima entrapment or barren plateaus by utilizing physically motivated structure rather than unconstrained parameter search. Despite this, the Guided Quantum Walk (GQW) has never been used for portfolio optimization or tested on existing noisy quantum hardware. In this paper we propose a hybrid quantum-classical solver for portfolio optimization that integrates Guided Quantum Walks (GQW) with domain-specific knowledge elicited from real Indian equity data. The core technical contributions are threefold. First, we implement a parameterized GQW circuit in Qiskit (v2.2) with a B\'{e}zier-curve-parameterized hopping rate schedule, mapping the portfolio selection problem directly to the GQW Hilbert space via an Ising Hamiltonian encoding. Second, we introduce a problem-aware warm-start strategy that initializes the energy scale parameters from classical sampling of the feasible portfolio subspace, bypassing the high-energy exploration phase that characterizes naive initialization. Third, we incorporate Conditional Value-at-Risk (CVaR) aggregation into the quantum walk measurement to improve solution space sampling, as well as a hardware-adaptive pipeline that adjusts concentration to per-backend circuit fidelity for IBM Heron devices.\\Our simulation results demonstrate near-optimal approximation ratios exceeding 0.99 for problem sizes up to N=20 on a noiseless setting with CVaR concentration \(((\alpha \in \{0.1,0.25\}))\), significantly outperforming standard energy expectation values \(((\alpha=1.0))\). Hardware validation on IBM Heron R2 processors, confirms that parameters optimized on noiseless simulation transfer effectively to real devices without re-optimization, with median approximation ratios above 0.85 across all backends for N=12 drawn from live NIFTY 50 market data. This constitutes the first end-to-end GQW implementation for financial portfolio optimization using IBM quantum hardware, and its application as a scalable quantum solver for real-world financial decision support systems.
Abstract Recent research on quantum walk-based optimization has shown theoretical potential as an alternative to variational algorithms, avoiding local minima entrapment or barren plateaus by utilizing physically motivated structure rather than unconstrained parameter search. Despite this, the Guided Quantum Walk (GQW) has never been used for portfolio optimization or tested on existing noisy quantum hardware. In this paper we propose a hybrid quantum-classical solver for portfolio optimization that integrates Guided Quantum Walks (GQW) with domain-specific knowledge elicited from real Indian equity data. The core technical contributions are threefold. First, we implement a parameterized GQW circuit in Qiskit (v2.2) with a B'{e}zier-curve-parameterized hopping rate schedule, mapping the portfolio selection problem directly to the GQW Hilbert space via an Ising Hamiltonian encoding. Second, we introduce a problem-aware warm-start strategy that initializes the energy scale parameters from classical sampling of the feasible portfolio subspace, bypassing the high-energy exploration phase that characterizes naive initialization. Third, we incorporate Conditional Value-at-Risk (CVaR) aggregation into the quantum walk measurement to improve solution space sampling, as well as a hardware-adaptive pipeline that adjusts concentration to per-backend circuit fidelity for IBM Heron devices.\Our simulation results demonstrate near-optimal approximation ratios exceeding 0.99 for problem sizes up to N=20 on a noiseless setting with CVaR concentration (((\alpha \in {0.1,0.25}))), significantly outperforming standard energy expectation values (((\alpha=1.0))). Hardware validation on IBM Heron R2 processors, confirms that parameters optimized on noiseless simulation transfer effectively to real devices without re-optimization, with median approximation ratios above 0.85 across all backends for N=12 drawn from live NIFTY 50 market data. This constitutes the first end-to-end GQW implementation for financial portfolio optimization using IBM quantum hardware, and its application as a scalable quantum solver for real-world financial decision support systems.
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.
We introduce SamBa-GQW, a novel quantum algorithm for solving binary combinatorial optimization problems of arbitrary degree with no use of any classical optimizer. The algorithm is based on a continuous-time quantum walk on the solution space represented as a graph. The walker explores the solution space to find its way to vertices that minimize the cost function of the optimization problem. The key novelty of our algorithm is an offline classical sampling protocol that gives information about the spectrum of the problem Hamiltonian. Then, the extracted information is used to guide the walker to high quality solutions via a quantum walk with a time-dependent hopping rate. We investigate the performance of SamBa-GQW on several quadratic problems, namely MaxCut, maximum independent set, portfolio optimization, and higher-order polynomial problems such as LABS, MAX- k -SAT and a quartic reformulation of the travelling salesperson problem. We empirically demonstrate that SamBa-GQW finds high quality approximate solutions on problems up to a size of n = 30 qubits by only sampling poly( n ) states among 2 n possible decisions. Furthermore, SamBa-GQW compares in par with classically optimized variational approaches, such as the variational guided quantum walk and QAOA (the latter when run on deep circuits). This places Samba-GQW as a promising heuristic to tackle combinatorial problems beyond the NISQ regime.
Quantum combinatorial optimization offers theoretical advantages for complex financial modeling, but physical implementation on Noisy Intermediate Scale Quantum (NISQ) devices is severely constrained by hardware topology. This study presents a hardware benchmarking analysis between a Hardware Efficient Variational Quantum Neural Network (HE-VQNN) and the Warm Start Quantum Approximate Optimization Algorithm (WS-QAOA) for a hybrid Mean Variance and Conditional Value at Risk (CVaR) portfolio objective. By implementing a novel classical quantum hybrid proxy matrix to bypass the CVaR auxiliary qubit bottleneck, we map up to 16 assets from the NIFTY 50 index onto an IBM heavy hex processor. We systematically quantify algorithmic resilience to the "SWAP tax" incurred during routing. Empirical results reveal a critical operational trade-off: WS-QAOA provides exact theoretical mapping but suffers catastrophic hardware decoherence due to exponential nonlocal gate overhead. Conversely, HE-VQNN preserves hardware coherence but lacks the mathematical expressibility to capture dense tail risk asset correlations. This study exposes the limitations of dense financial optimization on current architectures forces an nonviable choice between algorithmic inexpressibility and hardware decoherence. This is indicative of a deeper limitation as to what can and cannot be done with NISQ computers lacking in all-to-all connectivity.
Despite rapid progress in quantum optimization, broad real-hardware benchmarks comparing multiple algorithmic families across diverse combinatorial problems under a common protocol remain limited. We benchmark gate-based quantum optimization on four NP-hard problems: multi-dimensional knapsack (MDKP), maximum independent set (MIS), quadratic assignment (QAP), and market-share (MSP). We study VQE, CVaR-VQE, standard, multi-angle, and warm-start QAOA, together with qubit-efficient PCE and QRAO, on IBM Heron r1/r2 processors using resilience-level-2 mitigation. To our knowledge, this includes the first real-hardware QRAO results and the first multi-problem PCE hardware benchmark.
Across 247 method-instance combinations, we report transpiled circuit size, hardware outcomes, and an independent-error gate-count fidelity proxy, Fest. For MDKP and MIS, an empirical operating point near Fest≈0.1, corresponding to about 770 two-qubit gates at the median Heron-r2 CZ error rate, marks the onset of noise-dominated execution. QAP exposes a separate bottleneck: dense one-hot encodings and an exponentially sparse feasible manifold, with feasible fraction 10!/2100 at n=10; no tested hardware method produces a feasible assignment. Compiled QAOA-family circuits are generally noise dominated, and a matched uniform-random control shows that most feasible low-fidelity outcomes fall within the random range, apart from one finite-sample MIS warm-start exception. A SWAP-aware, fractional-gate, Nighthawk-topology compilation counterfactual reduces two-qubit counts but leaves all circuits below Fest=10−3. These conclusions apply to the tested implementations rather than QAOA in general. Qubit-efficient methods extend runnable instance sizes, but only within the empirical fidelity budget.
The increasing complexity of financial markets has heightened the demand for advanced computational methods capable of optimizing portfolios under multi-dimensional constraints involving risk, return, diversification, and liquidity. Traditional optimization frameworks, such as mean-variance analysis and heuristic meta-optimization, are limited by their scalability and sensitivity to non-convex, high-dimensional data structures. This study explores the application of quantum algorithms to portfolio optimization, demonstrating how Quantum Approximate Optimization Algorithm (QAOA), Quantum Annealing, and Variational Quantum Eigensolver (VQE) can address computational bottlenecks inherent in classical approaches. Quantum computation offers the potential to encode complex financial systems as Hamiltonian functions, allowing parallel exploration of vast solution spaces through superposition and entanglement. This enables faster convergence toward optimal portfolio allocations while simultaneously accounting for multi-factor correlations and dynamic market conditions. The research further investigates the role of hybrid quantum–classical optimization pipelines, in which quantum solvers perform core optimization tasks while classical systems manage data preprocessing and constraint validation. Empirical modeling and simulation indicate that quantum-based approaches can outperform conventional methods in risk-adjusted return optimization, efficient frontier computation, and real-time portfolio rebalancing. By bridging the gap between quantum computing and financial engineering, this study contributes to the development of next-generation financial analytics systems, aligning with the broader goal of achieving more adaptive, transparent, and data-resilient financial decision-making.
Variational quantum algorithms are increasingly explored for optimization problems at scales relevant to near-term quantum devices. Their practical performance depends strongly on design choices such as the sampling objective, classical optimizer, and ansatz layout before and after hardware transpilation. We study these factors for dynamic portfolio optimization, a multi-period financial problem balancing return, risk, transaction costs, cash-interest effects, and constraints. Using a sampling-based VQA framework on a 150-qubit dynamic portfolio instance, we evaluate several components of the optimization workflow. We propose a specific adaptive CVaR schedule that gradually tightens the sampled tail used for optimization, together with a two-stage optimizer combining global exploration with Particle Swarm Optimization and local refinement with the Nakanishi-Fujii-Todo optimizer. We also study ansatz depth and sequential growth strategies. Finally, we introduce two hardware-aware ansatz-layout modifications: a data-guided colored layout that assigns correlated variables to qubits connected by entangling gates, and a heavy-hex-native deep-chain layout designed to increase native two-qubit interaction depth without additional routing overhead after transpilation. Simulator studies select CVaR, optimizer, and depth configurations, while the ansatz comparison is performed on the ibm_quebec QPU. The results show that sampling strategy, optimizer scheduling, and hardware-aware layout design materially affect performance. In the reported QPU layout comparison, the proposed heavy-hex-native deep-chain layout achieves the best final objective value and CVaR-tail performance among the tested layouts. Although we do not observe quantum advantage over a state-of-the-art exact classical solver, our results provide practical guidance for improving VQA performance on near-term hardware.