A Comparative Study of Hybrid Quantum and Classical Genetic Algorithms in Portfolio Optimization
Romeu Rossi Junior, José Augusto Miranda Nacif, Leonardo Antônio Mendes Souza, Marcus Henrique Soares Mendes
Abstract
This work investigates the performance of a Hybrid Quantum Genetic Algorithm (HQGA) compared to a classical Genetic Algorithm (GA) for solving the portfolio optimization problem. Our results indicate that the HQGA converges faster to the optimal solution than its classical counterpart, while also maintaining a higher level of population diversity throughout the optimization process. In addition, the HQGA requires significantly fewer evaluations-to-solution than a brute-force approach to reach the global optimum.
AI Impact Assessments
(3 models)Scientific Impact Assessment
Core Contribution
This paper applies the Hybrid Quantum Genetic Algorithm (HQGA), originally proposed by Acampora and Vitiello (2021), to the Markowitz mean-variance portfolio optimization problem and compares its performance against a classical Genetic Algorithm (GA). The central claim is that HQGA converges faster, maintains higher population diversity, and requires fewer fitness evaluations than the classical GA. The paper does not propose a new algorithm; rather, it evaluates an existing one on a specific application domain.
Methodological Rigor
The experimental methodology has several significant weaknesses:
Problem scale: The experiments are limited to 9-asset subsets from the S&P 500, yielding a search space of only 2^9 = 512 possible portfolios. This is a trivially small combinatorial space that can be exhaustively enumerated. The paper itself acknowledges comparing against brute-force evaluation of all 512 portfolios, which undercuts the motivation for using sophisticated optimization algorithms. At this scale, the problem does not meaningfully test algorithmic capabilities.
Simplistic problem formulation: The binary formulation (include/exclude assets with no weight optimization) is a significant simplification of real portfolio optimization. Standard practice involves continuous weight allocation, cardinality constraints, transaction costs, and other realistic features. The equal-weight binary formulation limits practical relevance.
Limited experimental design: Only five randomly selected 9-asset subsets are tested. The statistical robustness of the comparison is questionable with such a small number of problem instances. Additionally, population sizes appear limited (pop=3 is highlighted), which is unusually small for meaningful evolutionary computation benchmarking.
Diversity metric limitations: The diversity metric (f_max - f̄) is a fitness-space measure that does not capture genotypic diversity. Two populations with identical genotypes but different fitness landscapes could yield different diversity readings. More established diversity metrics (Hamming distance, entropy-based measures) would strengthen the analysis.
Missing critical details: The paper does not specify key parameters such as the risk-aversion coefficient γ, the number of independent runs per configuration, mutation probability settings, or the specific quantum elitism variant used. The classical GA's configuration (selection method, crossover type, crossover/mutation rates) is not described, making the comparison potentially unfair and certainly irreproducible.
No quantum hardware execution reported: Despite the HQGA being designed for quantum hardware, all experiments appear to be simulated classically. The paper does not discuss whether simulations were performed, which quantum simulator was used, or how noise was handled — a critical omission for a quantum computing paper in 2026.
Statistical analysis: No statistical tests are reported to determine whether observed differences are significant. Standard deviations are shown in plots but no hypothesis testing is conducted.
Potential Impact
The practical impact of this work is limited for several reasons:
1. The problem scale (9 assets) is far from real-world portfolio optimization scenarios involving hundreds or thousands of assets.
2. The binary formulation without portfolio weights is not representative of actual investment practice.
3. Without quantum hardware results, the paper cannot speak to the practical viability of HQGA on NISQ devices.
4. The comparison is only against a basic classical GA, not against state-of-the-art portfolio optimization methods (e.g., quadratic programming, QAOA, VQE, simulated annealing, or other metaheuristics).
Timeliness & Relevance
The topic sits at the intersection of quantum computing and financial optimization, which is indeed a timely research area. However, the paper's execution does not advance the state of knowledge meaningfully. Several recent works cited by the authors (references [44-49]) have already explored quantum and quantum-inspired approaches to portfolio optimization with greater sophistication and scale.
Strengths
1. Clear exposition: The paper provides a well-organized description of quantum computing fundamentals and the HQGA algorithm, making it accessible to readers unfamiliar with quantum evolutionary computation.
2. Relevant research question: Investigating premature convergence resistance is a valid and interesting angle for quantum evolutionary algorithms.
3. Systematic comparison structure: Testing across multiple asset sets with different population sizes provides some breadth.
Limitations
1. No algorithmic novelty: The HQGA is taken directly from prior work [41]; the paper's contribution is purely empirical application.
2. Trivial problem size: 512-element search spaces do not require sophisticated optimization.
3. Incomplete benchmarking: No comparison against QAOA, VQE, simulated annealing, or even random search.
4. Reproducibility concerns: Missing parameter specifications and unclear simulation environment.
5. No scalability analysis: No discussion of how HQGA would perform as asset count grows, which is the critical question for practical applications.
6. Figures are referenced but content is limited: The convergence and diversity figures are described but the paper does not provide quantitative tables summarizing results across configurations.
7. Overclaiming: Statements like "practical advantages over classical GAs" are not supported by the evidence at this scale.
Overall Assessment
This paper represents an incremental empirical study applying an existing quantum algorithm to a small-scale instance of a well-known problem. While the writing is clear and the research question about diversity preservation is relevant, the experimental design is insufficient to draw meaningful conclusions about the practical advantages of HQGA. The problem scale is too small, the baselines too limited, and critical experimental details are missing. The work would benefit substantially from larger problem instances, comparison against multiple classical and quantum baselines, execution on actual quantum hardware, and rigorous statistical analysis.
Generated Apr 14, 2026
Comparison History (38)
Paper 2 has broader cross-disciplinary impact, bridging quantum computing and finance. Its focus on portfolio optimization offers direct real-world applications, whereas Paper 1 is highly theoretical and confined to a niche area of quantum optics. The timeliness of quantum algorithms for practical optimization problems gives Paper 2 a higher potential for widespread citation and practical adoption.
Paper 2 addresses a fundamental challenge in quantum physics (preparing Dicke states) using advanced counterdiabatic driving techniques. Its findings have broad, foundational implications across multiple cutting-edge fields, including quantum metrology, communication, and information processing. In contrast, Paper 1 applies a hybrid quantum genetic algorithm to a specific financial problem (portfolio optimization); while useful, its theoretical depth and cross-disciplinary impact appear more limited compared to the fundamental advancements proposed in Paper 2.
Paper 2 likely has higher scientific impact: it provides analytical solutions and general theoretical results for driven Markovian quantum oscillators, connects driven/non-driven Liouvillians via unitary displacement, and analyzes exceptional points—topics broadly relevant to open quantum systems, non-Hermitian physics, quantum optics, and control. Its methodological rigor and cross-field applicability are strong and timely. Paper 1 applies a hybrid quantum-classical GA to portfolio optimization; while potentially useful, impact depends on demonstrated quantum advantage and scalability, which the abstract does not substantiate beyond faster convergence vs a classical GA and brute force.
Paper 1 addresses a fundamental problem in quantum mechanics—the measurement problem—by proposing a continuous nonlinear evolution to replace instantaneous state reduction while preserving no-signaling. This has deep theoretical implications for quantum foundations, potentially impacting interpretations of quantum mechanics and quantum information theory. Paper 2 is an incremental comparative study applying a hybrid quantum-classical genetic algorithm to portfolio optimization, a well-explored application domain, offering limited novelty beyond benchmarking. Paper 1's foundational contribution has broader and more lasting impact potential.
Paper 1 addresses a fundamental question about the relationship between classical and quantum mechanics, rigorously demonstrating limitations of a recent proposal to reconstruct quantum wave functions from classical action branches. It covers deep physical phenomena (tunneling, Berry phase, flux quantization, Josephson effects) with broad implications for quantum foundations. Paper 2 presents an incremental comparative study of hybrid quantum-classical genetic algorithms for portfolio optimization—a well-explored application area—with limited novelty and narrower scope of impact.
Paper 2 addresses quantum-classical hybrid algorithms for portfolio optimization, a topic with broader interdisciplinary impact spanning quantum computing, finance, and optimization. It demonstrates practical advantages (faster convergence, fewer evaluations) of hybrid quantum approaches in a widely studied problem domain. Paper 1, while useful for network engineering, addresses a narrower infrastructure optimization problem (hollow-core fiber placement for QKD) with more limited audience and applicability. Paper 2's relevance to the growing quantum computing and financial technology fields gives it higher potential impact.
Paper 2 presents a broadly applicable, conceptually novel theoretical framework: a low-order hierarchy of Bargmann invariants yielding the first universal pairwise criterion for set coherence and a complete test for arbitrary finite families. This advances quantum information theory with rigorous, dimension-sensitive results and connects trace invariants to noncommutativity, likely impacting multiple subareas (resource theories, state compatibility, quantum foundations). Paper 1 targets a narrower application (portfolio optimization) and, while timely, hybrid quantum-classical GA improvements may be incremental and sensitive to implementation details, limiting broader scientific impact.
Paper 2 has higher potential impact due to its foundational novelty and rigor: it resolves incomplete mathematical conditions for KAK decompositions, clarifies conflicting definitions, and corrects a widespread geometric claim for SU(4) equivalence classes. These results can propagate broadly across Lie theory and quantum computing (quantum gate classification, circuit synthesis, invariants), providing durable infrastructure for future work. Paper 1 is more application-oriented but appears incremental (hybrid GA vs GA) and likely sensitive to problem instances and near-term hardware constraints, limiting breadth and longevity compared to a general theorem and classification framework.
Paper 1 likely has higher scientific impact: it synthesizes and evaluates a broad set of non-Markovian quantum jump unraveling methods, a timely topic driven by experimental advances where Markov approximations fail. As a comprehensive review filling a stated gap, it can become a key reference across open quantum systems, quantum information, and numerical simulation communities. Paper 2 targets a narrower application (portfolio optimization) and, without methodological details or clear quantum advantage evidence, its impact and rigor are harder to assess and likely more limited across fields.
Paper 2 offers a broadly applicable, experimentally accessible framework (tomogram-based nonclassicality quantifiers directly from homodyne data) and validates it across multiple states, nonlinear media (Kerr/cubic), and realistic decoherence via Lindblad dynamics. This combination of methodological rigor, clear experimental feasibility, and relevance to quantum technology (monitoring nonclassical resources under noise) suggests wider cross-field impact (quantum optics, metrology, information) than Paper 1, which appears more incremental and likely limited by near-term quantum advantage uncertainty in hybrid quantum GA portfolio optimization.
Paper 2 addresses fundamental interpretive questions in quantum mechanics—the measurement problem, nonlocality, Wigner's friend scenarios, and the nature of quantum facts—topics of deep and enduring significance across physics and philosophy of science. Its novel perspectival approach to resolving core foundational problems has broad intellectual impact. Paper 1, while useful, represents an incremental application of hybrid quantum-classical algorithms to a well-studied optimization problem, with narrower scope and more limited conceptual contribution to the field.
Paper 1 addresses a fundamental question in quantum mechanics—recurrence times for finite quantum systems—with rigorous mathematical results connecting to number theory (Dirichlet's approximation theorem). This has broad theoretical implications across quantum information, statistical mechanics, and mathematical physics. Paper 2 presents an incremental comparative study of hybrid quantum-classical genetic algorithms for portfolio optimization, a relatively well-explored application area, with limited novelty beyond showing faster convergence. Paper 1's foundational nature and cross-disciplinary mathematical depth give it greater long-term scientific impact.
Paper 1 demonstrates higher scientific impact by providing a rigorous, unifying representation-theoretic framework for nonlocal games, a foundational concept in quantum information. While Paper 2 offers practical applications in finance, its methodology represents an incremental comparative study of existing algorithms. Paper 1's synthesis of multiple mathematical viewpoints (e.g., NPA hierarchy, Bell-functional formulations) advances fundamental quantum theory, promising broader, long-term impact across device-independent quantum technologies and theoretical physics compared to the narrower, applied scope of Paper 2.
Paper 1 explores hybrid quantum-classical algorithms for portfolio optimization, addressing a highly relevant, real-world application in finance. The intersection of quantum computing and financial modeling is currently a rapidly growing field with immense industry interest. While Paper 2 offers a rigorous foundational mathematical analysis of quantum uncertainty relations, Paper 1 demonstrates broader immediate applicability, timeliness, and cross-disciplinary impact, making it more likely to influence both applied research and practical implementations.
Paper 1 presents a highly practical application of quantum computing to a real-world problem (portfolio optimization), offering measurable performance improvements over classical methods. This bridges multiple disciplines (quantum computing, finance, optimization) and aligns with the timely push for practical quantum advantage. In contrast, Paper 2 focuses on theoretical quantum foundations and metaphysics, which, while intellectually valuable, generally has a narrower scope and lacks direct real-world applicability or immediate technological impact.
Paper 1 likely has higher impact due to stronger real-world applicability (portfolio optimization/finance) and timeliness in hybrid quantum-classical optimization. Comparing HQGA vs classical GA with performance metrics (convergence, diversity, evaluations-to-solution) suggests actionable methodological outcomes transferable to other combinatorial optimization domains. Paper 2 offers a more theory-focused coherence analysis of Simon’s algorithm using specific coherence measures; while novel, its practical downstream impact is narrower and less directly enabling for applications beyond quantum information theory.
Paper 2 has higher estimated scientific impact due to its broader, foundational relevance: Hamiltonian chaos underpins large areas of nonlinear dynamics and quantum chaos, with cross-field implications (physics, applied math, dynamical systems, semiclassics). Its tools and conceptual framework can influence many subsequent studies and applications. Paper 1 is timely and applied, but likely narrower in scope and impact: hybrid quantum-classical genetic algorithms for portfolio optimization depend on near-term quantum practicality and may offer incremental gains over established heuristics without clear methodological rigor from the abstract alone.
Paper 2 addresses a broadly relevant, practical gap in quantum computing adoption by providing a structured procurement framework applicable across many institutions. Its comprehensive comparison of five hardware families and five capability layers offers lasting reference value. Paper 1, while competent, presents an incremental hybrid quantum-classical comparison on a well-studied problem (portfolio optimization) with limited novelty. Paper 2's breadth of impact across institutional planning, policy, and multiple quantum hardware paradigms gives it higher potential influence despite being less technically deep.
Paper 1 addresses a fundamental and technically challenging problem in few-body quantum scattering theory—extending the Faddeev formalism to the double continuum. This represents a significant methodological advance in nuclear/atomic physics with broad applications. Paper 2 presents an incremental comparison of hybrid quantum-classical vs. classical genetic algorithms for portfolio optimization, a well-studied problem, showing modest improvements (faster convergence, more diversity) without demonstrating quantum advantage on real hardware. The novelty and methodological depth of Paper 1 give it higher lasting scientific impact.
Paper 1 explores the application of hybrid quantum-classical algorithms to a significant real-world problem (portfolio optimization). This cross-disciplinary approach bridges quantum computing and finance, offering practical, near-term applications. In contrast, Paper 2 focuses on a highly specialized, theoretical problem in quantum field theory, which, while valuable to its specific subfield, is less likely to have broad, cross-disciplinary impact or immediate practical applications.