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arXiv:2606.10098

VQA for Dynamic Portfolio Optimization: Sampling Strategies, Optimizer Scheduling, and Hardware-Aware Ansatz Design

Mohammad Kashfi Haghighi

cs.CEquant-phSubmitted Jun 8, 2026• Announced Jun 10, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

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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.
We present a scalable, hardware-aware methodology for extending the Variational Quantum Eigensolver (VQE) to large, realistic Dynamic Portfolio Optimization (DPO) problems. Building on the scaling strategy from our previous work, where we tailored a VQE workflow to both the DPO formulation and the target QPU, we now put forward two significant advances. The first is the implementation of the Ising Sample-based Quantum Configuration Recovery (ISQR) routine, which improves solution quality in Quadratic Unconstrained Binary Optimization problems. The second is the use of the VQE Constrained method to decompose the optimization task, enabling us to handle DPO instances with more variables than the available qubits on current hardware. These advances, which are broadly applicable to other optimization problems, allow us to address a portfolio with a size relevant to the financial industry, consisting of up to 38 assets and covering the full Spanish stock index (IBEX 35). Our results, obtained on a real Quantum Processing Unit (IBM Fez), show that this tailored workflow achieves financial performance on par with classical methods while delivering a broader set of high-quality investment strategies, demonstrating a viable path towards obtaining practical advantage from quantum optimization in real financial applications.
The efficient and effective construction of portfolios that adhere to real-world constraints is a challenging optimization task in finance. We investigate a concrete representation of the problem with a focus on design proposals of an Exchange Traded Fund. We evaluate the sampling-based CVaR Variational Quantum Algorithm (VQA), combined with a local-search post-processing, for solving problem instances that beyond a certain size become classically hard. We also propose a problem formulation that is suited for sampling-based VQA. Our utility-scale experiments on IBM Heron processors involve 109 qubits and up to 4200 gates, achieving a relative solution error of 0.49%. Results indicate that a combined quantum-classical workflow achieves better accuracy compared to purely classical local search, and that hard-to-simulate quantum circuits may lead to better convergence than simpler circuits. Our work paves the path to further explore portfolio construction with quantum computers.
Abstract In-depth theoretical and practical research is nowadays being performed on variational quantum algorithms (VQAs), which have the potential to surpass traditional, classical, algorithms on a variety of problems, in physics, chemistry, biology, and optimization. Because they are hybrid quantum-classical algorithms, it takes a certain set of optimal conditions for their full potential to be exploited. For VQAs, the construction of an appropriate ansatz in particular is crucial, since it lays the ground for efficiently solving the particular problem being addressed. To prevent severe negative effects that hamper quantum computation, the substantial noise, together with the structural limitations, characteristic of currently available devices must be also taken into consideration while building the ansatz. In this work the effect of the quantum hardware structure, namely the topological properties emerging from the couplings between the physical qubits and the basis gates of the device itself, on the performances of VQAs is addressed. Specifically, it is here experimentally shown that a complex connectivity in the ansatz, albeit being beneficial for exploring wider sets of solutions, introduces an overhead of gates during the transpilation on a quantum computer that increases the overall error rate, thus undermining the quality of the training. It is hence necessary, when implementing a variation quantum learning algorithm, to find the right balance between a sufficiently parametrized ansatz and a minimal cost in terms of resources during transpilation. Moreover, the experimental finding allows to construct a heuristic metric function, which aids the decision-making process on the best possible ansatz structure to be deployed on a given quantum hardware, thus fostering a more efficient application of VQAs in realistic situations. The experiments are performed on two widely used variational algorithms, the VQE (variational quantum eigensolver) and the VQC (variational quantum classifier), both tested on two different problems, the first on the Markowitz portfolio optimization using real-world financial data, and the latter on a classification task performed on the Iris dataset.
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.
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 ((α∈{0.1,0.25}))((\alpha \in \{0.1,0.25\}))((α∈{0.1,0.25})), significantly outperforming standard energy expectation values ((α=1.0))((\alpha=1.0))((α=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.
We present an end-to-end pipeline for large-scale portfolio selection with cardinality constraints and experimentally demonstrate it on trapped-ion quantum processors using hardware-aware decomposition. Building on RMT-based correlation-matrix denoising and community detection, we identify correlated asset groups and introduce a correlation-guided greedy splitting scheme that caps each cluster by the executable qubit budget. Each cluster defines a hardware-embeddable QUBO subproblem that we solve using bias-field digitized counterdiabatic quantum optimization (BF-DCQO), a non-variational method that avoids classical parameter-training loops. We recombine low-energy candidates into global portfolios and enforce feasibility with a two-stage post-processing routine: fast repair followed by a cardinality-preserving swap local search. We benchmark the workflow on a 250-asset universe taken from the S&P 500 and execute subproblems on a 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. We observe that larger executable subproblem sizes reduce decomposition error and systematically improve final objective values and risk-return trade-offs relative to randomized baselines under identical post-processing. Overall, the results establish a hardware-tested route for scaling financial optimization problems, defined by a trade space in which executable problem size and circuit cost are balanced against the resulting solution quality.