[Paper Review] Quantum Machine Learning for Finance

Marco Pistoia, Syed Farhan Ahmad+11 more|arXiv (Cornell University)|Sep 9, 2021

Quantum Computing Algorithms and Architecture137 references11 citations

TL;DR

This paper reviews quantum machine learning (QML) algorithms tailored for financial applications, focusing on regression, classification, clustering, generative modeling, feature extraction, sequential decision-making, and NLP. It demonstrates that quantum algorithms can offer polynomial or potentially exponential speedups over classical counterparts, particularly in linear algebra-intensive tasks, while addressing practical challenges like data loading and hardware constraints in the NISQ era.

ABSTRACT

Quantum computers are expected to surpass the computational capabilities of classical computers during this decade, and achieve disruptive impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from Quantum Computing not only in the medium and long terms, but even in the short term. This review paper presents the state of the art of quantum algorithms for financial applications, with particular focus to those use cases that can be solved via Machine Learning.

Motivation & Objective

• To survey state-of-the-art quantum algorithms applicable to financial use cases, especially those solvable via machine learning.
• To identify financial applications where quantum speedup—particularly polynomial or exponential—can be achieved despite NISQ hardware limitations.
• To bridge the gap between general quantum machine learning research and finance-specific implementations, especially where literature is sparse.
• To analyze the practical feasibility of deploying quantum ML in finance, considering data loading, output readout, and algorithmic bottlenecks.
• To provide a roadmap for adopting quantum machine learning in financial services during the NISQ era and beyond.

Proposed method

• Surveying quantum algorithms for linear algebra, including HHL-type solvers for systems of linear equations, with complexity scaling as Õ(log N) under certain conditions.
• Applying quantum algorithms to supervised learning tasks such as L2 regression, classification, and clustering, leveraging quantum state preparation and amplitude amplification.
• Adapting variational quantum circuits (VQCs) and parameterized quantum circuits (PQCs) for NLP tasks like sentence similarity and sentiment analysis, enabling NISQ-compatible processing.
• Integrating quantum-enhanced feature extraction and dimensionality reduction techniques to reduce computational overhead in high-dimensional financial data.
• Using quantum nearest-neighbor algorithms to accelerate similarity computations in financial NLP, achieving O(√(MN) log M) complexity versus classical O(NM).
• Evaluating the impact of quantum speedups in real-world financial workloads, such as credit risk assessment, financial forecasting, and fraud detection, by mapping classical ML pipelines to quantum equivalents.

Experimental results

Research questions

• RQ1 Which financial machine learning tasks are most amenable to quantum speedup, and under what conditions can exponential or polynomial speedups be achieved?
• RQ2 How do hardware constraints of NISQ devices—such as qubit coherence, noise, and data loading limitations—affect the practical deployment of quantum ML in finance?
• RQ3 To what extent can existing general-purpose quantum machine learning algorithms be adapted to specific financial use cases like portfolio optimization, risk modeling, and credit scoring?
• RQ4 What are the key bottlenecks in end-to-end quantum ML pipelines for finance, and how can they be mitigated through algorithmic or architectural innovations?
• RQ5 Can quantum NLP techniques, such as the DisCo framework or quantum CSC models, outperform classical methods in financial text analysis tasks like sentiment detection or anomaly identification?

Key findings

• Quantum algorithms for linear systems (e.g., HHL) can solve regression problems in time Õ(log N), offering potential exponential speedup over classical O(N) methods under specific conditions.
• For L2 regression, Wang’s algorithm achieves classical solution recovery in poly(log N, d, κ, 1/ε) time, representing a significant polynomial speedup in data-processing subroutines.
• Quantum NLP techniques, such as the quantum nearest-neighbor algorithm in the DisCo framework, can classify sentences into M classes in O(√(MN) log M) time, outperforming classical O(NM) complexity.
• Variational quantum circuits enable efficient encoding of financial text and linguistic structures, making quantum NLP viable for NISQ devices.
• Despite theoretical speedups, practical quantum advantage remains limited by challenges in data loading (e.g., QRAM requirements) and output state readout, which often require O(d) copies of the quantum state.
• Applications in credit risk assessment, financial forecasting, and fraud detection show strong potential for quantum acceleration, particularly when leveraging quantum-enhanced NLP and clustering.