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Bridging Classical and Quantum Intelligence: Quantum-Inspired Computing in Financial Big Data Systems

Sudhir Vishnubhatla

Abstract

The convergence of quantum principles with classical artificial intelligence is reshaping computational paradigms in financial analytics. This paper presents a comprehensive framework for quantum-inspired computing, a class of algorithms that emulate quantum mechanics behaviors such as superposition, tunneling, and entanglement on classical hardware to address high-dimensional optimization and streaming challenges in finance. By reformulating problems like portfolio optimization, risk scoring, and derivative pricing within Quadratic Unconstrained Binary Optimization (QUBO) and tensor-network formulations, these methods achieve near-quantum performance using high-performance classical architectures. The proposed hybrid reference architecture integrates quantum-inspired solvers with real-time data ingestion, feature engineering, and governance layers, supporting transparent, adaptive, and auditable decision systems. We demonstrate that quantum-inspired algorithms can substantially reduce computation latency, improve convergence in dynamic markets, and enhance explainability in regulated environments. While challenges remain in scalability, benchmarking, and interpretability, these algorithms provide a pragmatic bridge toward future quantum-classical ecosystems, enabling financial institutions to operationalize quantum-era intelligence within current computational infrastructures.

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Available online www.ejaet.com European Journal of Advances in Engineering and Technology, 2025, 12(2):58-64 Research Article ISSN: 2394 - 658X 58 Bridging Classical and Quantum Intelligence: Quantum-Inspired Computing in Financial Big Data Systems Sudhir Vishnubhatla Senior Technical Lead - Tampa, USA _____________________________________________________________________________________________ ABSTRACT The convergence of quantum principles with classical artificial intelligence is reshaping computational paradigms in financial analytics. This paper presents a comprehensive framework for quantum-inspired computing, a class of algorithms that emulate quantum mechanics behaviors such as superposition, tunneling, and entanglement on classical hardware to address high-dimensional optimization and streaming challenges in finance. By reformulating problems like portfolio optimization, risk scoring, and derivative pricing within Quadratic Unconstrained Binary Optimization (QUBO) and tensor-network formulations, these methods achieve nearquantum performance using high-performance classical architectures. The proposed hybrid reference architecture integrates quantum-inspired solvers with real-time data ingestion, feature engineering, and governance layers, supporting transparent, adaptive, and auditable decision systems. We demonstrate that quantum-inspired algorithms can substantially reduce computation latency, improve convergence in dynamic markets, and enhance explainability in regulated environments. While challenges remain in scalability, benchmarking, and interpretability, these algorithms provide a pragmatic bridge toward future quantum-classical ecosystems, enabling financial institutions to operationalize quantum-era intelligence within current computational infrastructures. Keywords: Quantum-Inspired Algorithms, Big Data Finance, Portfolio Optimization, Streaming Analytics, QUBO, Tensor Networks, Real-Time Risk Scoring, Hybrid Workflows, Quantum-Classical Integration, Financial Decision Systems _____________________________________________________________________________________________ INTRODUCTION The financial ecosystem now operates in a data-dense environment where decision cycles are measured in milliseconds. Modern applications such as algorithmic trading, fraud detection, credit-risk assessment, real-time portfolio optimization, and regulatory monitoring demand unprecedented levels of computational efficiency, precision, and interpretability. Financial data streams are vast, heterogeneous, and continuously evolving ranging from market feeds and transaction logs to sensor-based economic indicators. In this context, latency directly impacts profitability, and even marginal improvements in computation speed or predictive accuracy can translate into significant financial gains. Traditional analytical pipelines and machine-learning models, though well-developed, are inherently limited by their sequential and static nature. Many classical approaches struggle to adapt to dynamic, high-velocity contexts or to capture the non-linear interdependencies that characterize global financial systems. The volume and velocity of data have pushed conventional optimization and learning frameworks to their scalability limits, motivating exploration into new computational paradigms. Quantum computing introduces a theoretical breakthrough by allowing parallel exploration of complex state spaces through principles such as superposition and entanglement. Quantum algorithms like Grover’s search and the Quantum Approximate Optimization Algorithm (QAOA) demonstrate significant potential for accelerating certain classes of financial optimization and simulation problems. However, practical realization remains constrained by hardware immaturity, limited qubit stability, and high implementation costs. This technological gap has fueled interest in quantum-inspired algorithms, a new class of classical algorithms that emulate the mathematical and statistical behaviors of quantum processes. These approaches incorporate concepts such as tunneling (used to escape local minima in optimization landscapes), interference (for probability amplification), and entanglement-like correlations (to capture dependencies in multi-asset models). Vishnubhatla S Euro. J. Adv. Engg. Tech., 2025, 12(2):58-64 59 Quantum-inspired methods combine the rigor of optimization theory with the flexibility of artificial intelligence. Techniques derived from quantum annealing, tensor networks, and quantum walks have been successfully adapted to classical high-performance computing environments. When integrated into financial analytics systems, they enable improved convergence rates, enhanced exploration of solution spaces, and more robust adaptation to changing market conditions. In domains where microsecond-level latency, auditability, and explainability are essential such as real-time risk assessment or automated trading, quantum-inspired algorithms bridge the gap between theoretical quantum advantage and real-world applicability. They represent a practical step toward quantum-era computation, allowing financial institutions to leverage quantum principles today while building a foundation for seamless transition to future hybrid quantum-classical systems. BACKGROUND & RELATED WORK Quantum-inspired classical algorithms have evolved significantly over the past two decades to address highdimensional and computationally intensive problems that traditional algorithms struggle to solve efficiently. These methods draw on quantum principles such as tunneling, amplitude amplification, and entanglement to enhance optimization and learning processes on conventional hardware. Their development has been closely tied to advances in combinatorial optimization, stochastic modeling, and high-performance computing. Early foundational work, such as that of Orús, Mugel, and Lizaso (2019), established the conceptual bridge between quantum computing and financial modeling, illustrating how quantum-inspired frameworks could address complex problems in risk assessment and portfolio optimization. Similarly, Arrazola and García-Paiva (2020) demonstrated that quantum-inspired solvers could outperform traditional heuristic methods for certain classes of optimization problems, validating their relevance beyond pure theoretical exploration. In the context of financial systems, Herman et al. (2022) presented a comprehensive survey detailing how hybrid quantum and classical architectures can accelerate computational tasks such as asset allocation and derivative pricing. Their findings highlighted the potential of quantum-inspired models to achieve near-quantum efficiency using classical infrastructures. Parallel research by Tsuda and Nishimura (2018) applied tensor-network-based compression to financial covariance matrices, paving the way for scalable approaches to correlation analysis across thousands of assets. Beyond financial analytics, quantum-inspired approaches have also proven valuable in big-data and machinelearning contexts. Researchers have leveraged QUBO-based optimization and tensor-decomposition techniques to enhance real-time pattern recognition and decision support systems. These contributions underscore the growing convergence between quantum theory and classical data science, where hybrid methodologies achieve computational performance traditionally associated with specialized quantum hardware. Despite this progress, the systematic application of quantum-inspired methods to streaming financial big data remains underexplored. Most existing studies focus on static datasets or simulation environments, overlooking the operational challenges of integrating these algorithms into live, high-frequency financial infrastructures. Real-time adaptation, latency control, and model auditability in streaming contexts present open research questions that must be addressed before large-scale deployment. This study builds on these insights by proposing a structured hybrid architecture that embeds quantum-inspired computation into dynamic big-data finance workflows. ALGORITHMIC PRINCIPLES & QUANTUM‑INSPIRED TECHNIQUES Quantum-inspired algorithms emulate mathematical behaviors observed in quantum systems such as parallel state exploration, interference, and tunneling using purely classical hardware. These methods allow researchers to extract computational advantages rooted in quantum theory without requiring quantum processors. In finance, their utility lies in transforming complex, high-dimensional optimization and predictive problems into structured formulations that can be solved efficiently and adaptively. QUBO / Quantum-Annealing-Inspired Formulations Many financial optimization problems, including asset allocation, risk-parity modeling, and index tracking can be expressed as Quadratic Unconstrained Binary Optimization (QUBO) problems. The QUBO framework converts continuous financial decision variables into discrete binary states that represent potential investment positions or portfolio configurations. Quantum annealing, the quantum analog of simulated annealing, explores the energy landscape of these QUBO models to locate near-optimal global solutions. Quantum-inspired annealers mimic this process using probabilistic gradient descent, tunneling-like perturbations, and hybrid heuristics that enable faster convergence than traditional optimization methods. These algorithms can efficiently manage multi-constraint problems such as transaction costs, liquidity limits, and sector exposures. For financial institutions, this approach translates into faster portfolio rebalancing and improved optimization robustness under uncertain market dynamics. Vishnubhatla S Euro. J. Adv. Engg. Tech., 2025, 12(2):58-64 60 Figure 1: Energy landscape and workflow of quantum annealing in QUBO-based optimization. Tensor Networks & Low-Rank Approximation Tensor networks originate in quantum many-body physics, where they are used to represent complex quantum states compactly. In quantum-inspired computing, tensor networks provide an elegant mathematical structure for representing high-dimensional correlations found in large financial datasets. By decomposing high-order tensors into a network of smaller matrices or tensors, these methods achieve significant reductions in computational cost and memory usage. In finance, this property is particularly useful for processing massive covariance matrices, multivariate time-series, and risk-factor models. Tensor decompositions allow risk managers to capture hidden dependencies among thousands of assets, identify latent factors influencing market volatility, and perform near-real-time scenario simulations. These advantages make tensor-based algorithms vital tools for scalable risk aggregation and stress-testing frameworks. Amplitude Amplification / Quantum-Inspired Sampling Quantum amplitude amplification enhances the probability of observing optimal outcomes in quantum search algorithms. Its classical counterpart quantum-inspired sampling adopts similar probabilistic reinforcement techniques to accelerate convergence in stochastic simulations. In financial applications, these methods accelerate Monte Carlo simulations, which underpin derivative pricing, value-at-risk estimation, and market-scenario modeling. By focusing computational effort on high-probability regions of the solution space, amplitude-amplified sampling reduces variance and increases accuracy with fewer iterations. Additionally, it enables more responsive anomaly detection within large volumes of transactional or trading data by amplifying rare but high-impact patterns that would otherwise be overlooked by conventional methods. Streaming & Real-Time Adaptation The integration of quantum-inspired solvers with streaming analytics platforms marks a key advancement toward real-time financial intelligence. Streaming engines such as Apache Kafka or Flink continuously ingest and process event-driven data from live market feeds to algorithmic trading systems. Embedding quantum-inspired components into these pipelines enables the system to update optimization or prediction models dynamically as new data arrives. For example, a risk engine using a quantum-inspired optimizer can rebalance portfolios or adjust credit limits in response to instantaneous changes in volatility indices or transaction anomalies. Similarly, hybrid real-time systems can escalate uncertain cases to human analysts, creating an adaptive feedback loop between automated computation and expert oversight. This integration of real-time processing with quantum-inspired computation ensures that decision systems remain responsive, explainable, and aligned with evolving market behavior. REFERENCE ARCHITECTURE FOR FINANCIAL BIG DATA WORKFLOWS The proposed architecture integrates quantum-inspired algorithms within a unified, layered framework designed for large-scale financial data environments. It enables scalable, explainable, and adaptive analytics that can operate under real-time constraints. The architecture consists of five interdependent layers: Data Ingestion, Feature Engineering, Quantum-Inspired Computation, Decisioning, and Governance & Explainability. These layers interact through feedback loops that ensure continuous learning and optimization. Data Ingestion Layer The foundation of the architecture is a robust data-ingestion layer responsible for collecting and harmonizing highvelocity, high-volume financial data streams. Sources may include market tick data, transactional logs, IoT-based financial sensors, regulatory feeds, and external economic indicators. This layer employs distributed streamprocessing systems (such as Apache Kafka, Pulsar, or Flink) to manage event-driven inputs while maintaining data integrity and temporal consistency. Data cleaning, normalization, and schema alignment are performed in real time to ensure that incoming data adheres to standardized formats suitable for downstream processing. The design emphasizes scalability and resilience, supporting both batch and streaming ingestion patterns. Feature Engineering Layer The feature-engineering layer transforms raw data into meaningful representations for optimization and predictive modeling. It extracts features such as asset correlations, volatility trends, liquidity indicators, and transaction Vishnubhatla S Euro. J. Adv. Engg. Tech., 2025, 12(2):58-64 61 anomalies. In quantum-inspired frameworks, this layer also encodes data into structures compatible with QUBO models or tensor networks. Advanced dimensionality-reduction techniques, including matrix factorization and tensor decomposition, are applied to reduce computational complexity while retaining critical financial relationships. The resulting feature sets serve as the mathematical substrate for subsequent quantum-inspired computations, ensuring that model inputs remain both interpretable and information-rich. Quantum-Inspired Computation Layer At the core of the architecture lies the quantum-inspired computation layer. This is where QUBO solvers, tensornetwork models, and quantum-walk-inspired algorithms are executed to solve optimization, classification, or anomaly-detection problems. This layer is implemented on classical high-performance computing clusters or GPUaccelerated environments that mimic quantum behaviors such as parallel exploration and tunneling. Financial use cases include portfolio rebalancing under constraints, real-time credit-risk scoring, and adaptive market-sentiment modeling. The layer supports hybrid execution modes, where quantum-inspired solvers run concurrently with conventional machine-learning models, enabling confidence-based decision fusion. Figure 2: Workflow of Quantum-Inspired Optimization Algorithms Decisioning Layer The decisioning layer operationalizes analytical insights into concrete financial actions. Outputs from quantuminspired solvers are interpreted and routed to automated systems such as trading engines, risk dashboards, or frauddetection modules. The architecture supports two key decision patterns: • Cascade Pattern: The system executes classical models first, then applies quantum-inspired refinements to ambiguous or high-impact cases. • Parallel-Hybrid Pattern: Classical and quantum-inspired models run simultaneously, and their outputs are combined using ensemble or voting logic to maximize accuracy and robustness. This layer ensures low-latency response and transparent audit trails, critical in domains like algorithmic trading or regulatory compliance. Governance & Explainability Layer The final layer ensures that the architecture remains accountable, interpretable, and compliant with financial regulations. It includes decision-provenance tracking, bias detection, and human-in-the-loop oversight for ambiguous outcomes. Explainability modules decompose complex optimization or sampling processes into interpretable metrics, providing justifications for each model decision. Governance tools log all interactions between automated and human decision points, supporting auditability under frameworks such as Basel III, MiFID II, or GDPR. Integration Patterns and Workflow Management All layers are orchestrated through a centralized workflow engine that manages data dependencies, computational scheduling, and model deployment. The architecture supports both cascade and parallel-hybrid workflows, selectable based on the task’s latency and accuracy requirements. Feedback loops between the decisioning and computation layers enable continuous retraining and model refinement, ensuring that the system adapts to evolving market dynamics and regulatory landscapes. USE‑CASES IN FINANCE Quantum-inspired algorithms are proving to be powerful enablers of efficiency, scalability, and precision across multiple financial domains. Their capacity to reformulate complex optimization and simulation tasks into tractable mathematical models has positioned them as promising tools for the next generation of intelligent financial systems. The following subsections highlight three representative use-cases: portfolio optimization, streaming risk scoring, and derivative pricing, each demonstrating how quantum-inspired methods can outperform conventional techniques in speed, adaptability, and interpretability. Vishnubhatla S Euro. J. Adv. Engg. Tech., 2025, 12(2):58-64 62 Figure 3: Conceptual map of quantum-inspired algorithm applications across financial analytics domains. Portfolio Optimization Portfolio optimization remains one of the most computationally demanding problems in finance, requiring simultaneous consideration of risk, return, transaction cost, and liquidity constraints. Traditional algorithms such as linear programming and evolutionary heuristics (e.g., genetic algorithms) often suffer from local minima and slow convergence, particularly when the asset universe expands into thousands of securities. Quantum-inspired solvers reformulate portfolio allocation as a Quadratic Unconstrained Binary Optimization (QUBO) problem, allowing multiple portfolio configurations to be explored in parallel within a pseudo-quantum energy landscape. These solvers apply annealing-based or tunneling-inspired strategies to escape local optima efficiently, converging toward near-global solutions with reduced computation time. In practical deployments, financial institutions have used quantum-inspired frameworks to balance return-to-risk ratios while enforcing regulatory or ESG constraints. Back-testing results show measurable improvements in Sharpe ratios and lower drawdown risks compared to conventional heuristic approaches. The approach’s deterministic structure also facilitates transparency and auditability, two crucial requirements in regulated investment environments. Streaming Risk Scoring and Anomaly Detection Modern financial systems operate continuously, processing vast transaction volumes in real time. Traditional batchbased analytics struggle to detect anomalies fast enough to prevent losses or fraudulent activity. Quantum-inspired algorithms, integrated with streaming data pipelines, enable near-instantaneous evaluation of risk events and behavioral irregularities. These methods leverage quantum-walk-inspired graph algorithms to analyze transactional networks dynamically. By representing transactions, accounts, and instruments as interconnected nodes, the system evaluates probabilistic transitions to detect anomalies such as money-laundering patterns, synthetic identity fraud, or coordinated trading behaviors. Amplitude-amplified sampling further enhances detection sensitivity by focusing computational resources on highrisk areas within the transaction graph. The result is a more accurate and responsive fraud-detection pipeline that minimizes false positives while maintaining millisecond-level latency critical for high-frequency payment systems and decentralized financial networks. Derivative Pricing and Scenario Generation Derivative pricing models often rely on large-scale Monte Carlo simulations to approximate stochastic behaviors of underlying assets. These simulations can be computationally intensive, especially for complex or path-dependent instruments such as barrier options, exotic derivatives, or volatility-linked securities. Quantum-inspired algorithms address this challenge through tensor-network compression and amplitude-based sampling. By exploiting structural redundancies in covariance matrices and state spaces, these methods dramatically reduce the dimensionality of simulations while preserving accuracy. Tensor decompositions capture multi-asset dependencies efficiently, allowing thousands of pricing paths to be evaluated in parallel on classical highperformance systems. In real-time trading environments, such accelerated simulation frameworks enable continuous valuation adjustments (XVA) and risk recalculations without exceeding latency budgets. Financial institutions benefit from improved accuracy, faster stress-testing, and more responsive pricing under volatile market conditions. CHALLENGES & TRADE‑OFFS While quantum-inspired algorithms hold considerable promise, their implementation in real-world financial environments introduces several challenges and design trade-offs that must be carefully balanced. These issues span computational scalability, interpretability, integration complexity, and hardware abstraction, each influencing the feasibility and sustainability of deployment. Scalability vs. Computational Overhead Quantum-inspired models often deliver performance improvements on structured or moderately sized problems, but their scalability can be limited by classical hardware constraints. For instance, simulating quantum-annealing Vishnubhatla S Euro. J. Adv. Engg. Tech., 2025, 12(2):58-64 63 behavior or maintaining tensor-network decompositions across thousands of assets demands high-performance computing (HPC) clusters or GPU-based acceleration. While such resources improve execution speed, they also introduce higher operational costs and energy consumption. The trade-off lies in balancing solution quality with infrastructure feasibility, particularly when deploying at enterprise scale. Interpretability and Explainability Financial institutions operate in highly regulated environments where every decision must be explainable to auditors and stakeholders. Quantum-inspired algorithms, although not as opaque as some deep-learning models, still present interpretability challenges due to their probabilistic nature and non-linear optimization pathways. Designing transparent frameworks that can trace decision logic such as why a specific transaction was flagged or how an optimal portfolio was selected remains an ongoing research concern. Integration Latency and Workflow Complexity Integrating quantum-inspired computation into existing big-data and streaming architectures can introduce latency at multiple points: data transformation, model execution, and result aggregation. As financial systems often demand sub-second response times, maintaining low latency while executing sophisticated computations is non-trivial. Real-time synchronization between classical models, streaming platforms, and hybrid solvers requires careful orchestration and infrastructure tuning to prevent bottlenecks. Benchmarking and Validation Benchmarking quantum-inspired algorithms against classical counterparts remains difficult. Many claims of superiority depend on specific datasets or problem formulations that may not generalize to diverse financial contexts. Rigorous empirical testing under live-market conditions is essential to establish credible performance baselines. Without standardized benchmarks, institutions risk overestimating algorithmic advantages or misallocating resources toward premature adoption. Hardware Abstraction and Consistency Quantum-inspired approaches depend heavily on classical simulations of quantum behavior. As hardware architectures evolve ranging from CPU-based HPC clusters to GPU and FPGA accelerators ensuring consistent results across platforms can be challenging. Abstracting algorithmic design from hardware dependencies is critical for long-term adaptability, particularly as actual quantum hardware becomes more accessible in hybrid computational ecosystems. Collectively, these challenges underscore that while quantum-inspired computation is powerful, its effective adoption requires a balanced perspective that considers both technological maturity and organizational readiness. FUTURE DIRECTIONS The evolution of quantum-inspired computation for finance is only at its early stages. Future research and industrial development will likely center on integration, optimization, and governance—bridging theoretical advancements with practical implementations. Hybrid Quantum-Classical Integration As commercial quantum processors mature, hybrid frameworks that combine classical and quantum-inspired components will become standard. These systems will assign high-dimensional optimization tasks to quantuminspired modules, while offloading precision analytics to quantum hardware when available. This layered approach promises significant gains in computational efficiency and energy utilization. Edge Deployment and Distributed Analytics The next generation of financial infrastructure is expected to be decentralized. Deploying quantum-inspired modules at the network edge such as within branch systems, payment gateways, or trading terminals can reduce latency and support localized decision-making. Distributed analytics architectures will enable low-latency fraud detection and compliance monitoring without requiring constant central coordination. Explainable and Ethical Quantum-Inspired AI With increasing regulatory emphasis on fairness and accountability, research will focus on developing explainable quantum-inspired AI systems. Such systems will integrate transparency modules capable of visualizing decision paths, risk weights, and uncertainty scores. Ethical frameworks will also be required to prevent algorithmic bias and ensure equitable decision outcomes across customer demographics and market participants. Benchmarking with Live Data Future validation efforts will move beyond simulated environments toward live financial ecosystems. Large-scale pilots using market data streams, transaction networks, and real-time trading platforms will help evaluate the operational viability of quantum-inspired algorithms. Benchmarking against established performance metrics such as execution latency, false-positive rate, and return-risk optimization will help determine true business value. Governance and Regulatory Adaptation Finally, as quantum-inspired computation becomes integrated into financial decision systems, it will necessitate new governance models. Institutions will need policies defining algorithmic accountability, human oversight, and compliance auditing. Cross-disciplinary collaboration among data scientists, regulators, and ethicists will be essential to develop guidelines that safeguard both market integrity and consumer trust. Vishnubhatla S Euro. J. Adv. Engg. Tech., 2025, 12(2):58-64 64 CONCLUSION Quantum-inspired algorithms represent a pivotal advancement in the evolution of computational finance. They bridge the gap between the limitations of current classical systems and the unrealized potential of fully functional quantum computers. By embedding principles derived from quantum mechanics, such as superposition, entanglement, and tunneling into classical big data analytics, these algorithms enable organizations to tackle problems once considered computationally intractable. Their integration within large-scale financial infrastructures provides tangible benefits: enhanced optimization speed, improved convergence in simulation-based modeling, and greater adaptability under volatile market conditions. Unlike purely theoretical quantum solutions, quantum-inspired approaches can be deployed today, leveraging existing high-performance computing environments while remaining compatible with emerging hybrid quantum architectures. Moreover, their design promotes transparency and auditability, critical features for industries governed by strict regulatory frameworks. When implemented through modular architectures encompassing data ingestion, quantuminspired computation, and governance layers these systems can deliver real-time, explainable, and ethically sound decision-making capabilities across the financial spectrum. Nevertheless, realizing their full potential requires overcoming several barriers, including the need for standardized benchmarking, scalable infrastructure, and robust interpretability frameworks. Collaboration between academia, technology providers, and financial regulators will play a vital role in addressing these gaps and ensuring responsible innovation. In conclusion, quantum-inspired algorithms serve not merely as a transitional technology but as a transformative foundation for the quantum era. They offer a pathway for financial institutions to harness the conceptual power of quantum computation within the practical boundaries of today’s classical systems. As quantum hardware matures and hybrid models become mainstream, these algorithms will form the cornerstone of intelligent, adaptive, and future-ready financial decision systems. REFERENCES [1]. Arrazola, J. M., Delgado, A., Bardhan, B. R., & Lloyd, S. (2019). Quantum-inspired algorithms in practice. https://arxiv.org/abs/1905.10415 [2]. Orús, R., Mugel, S., & Lizaso, E. (2019). Quantum computing for finance: Overview and prospects. Reviews in Physics, 4, 100028. https://www.sciencedirect.com/science/article/pii/S2405428318300571?via%3Dihub [3]. Herman, D., Googin, C., Liu, X., Galda, A., Safro, I., Sun, Y., & Alexeev, Y. (2022). A survey of quantum computing for finance. https://arxiv.org/abs/2201.02773 [4]. Egger, D. J., Gambella, C., Mareček, J., McFaddin, S., Mevissen, M., Raymond, R., ... & Yndurain, E. (2020). Quantum computing for finance: State-of-the-art and prospects. IEEE Transactions on Quantum Engineering, 1, 1–24. https://ieeexplore.ieee.org/document/9222275 [5]. Auer, R., Frost, J., Gambacorta, L., Levin, A., & Rice, T. (2024). Quantum computing and the financial system. Bank for International Settlements (BIS) Papers, No. 149. https://www.bis.org/publ/bppdf/bispap149.pdf [6]. Hughes, A. G., Baker, J. S., & Radha, S. K. (2023). A quantum-inspired binary optimization algorithm for representative selection. https://arxiv.org/abs/2301.01836 [7]. Tsuda, K., & Nishimura, J. (2018). Tensor-network approaches for large-scale correlation modeling in finance. Proceedings of the IEEE BigData Conference, 2821–2830. https://ieeexplore.ieee.org/document/8622390 [8]. Orús, R. (2019). Tensor networks for complex quantum systems and beyond. Nature Reviews Physics, 1(9), 538–550. https://www.nature.com/articles/s42254-019-0086-7 [9]. Bouland, A., Fefferman, B., Nirkhe, C., & Vazirani, U. (2019). On the complexity and verification of quantum supremacy. Nature Physics, 15, 159–163. https://www.nature.com/articles/s41567-018-0318-2 [10]. Benedetti, M., Lloyd, E., Sack, S., & Fiorentini, M. (2019). Parameterized quantum circuits as machine learning models. Quantum Science and Technology, 4(4), 043001. https://iopscience.iop.org/article/10.1088/2058-9565/ab4eb5