# Quantum versus Classical Generative Modelling in Finance

arXiv: https://arxiv.org/abs/2008.00691 · HTML: https://mlsanity.com/paper/2008.00691/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2020.

## Built on by (most cited first, 21 of 21)

- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (2021)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Trainability barriers and opportunities in quantum generative modeling](https://mlsanity.com/paper/2305.02881/) (2023)
- [Variational inference with a quantum computer](https://mlsanity.com/paper/2103.06720/) (2021)
- [Benchmarking simulated and physical quantum processing units using quantum and hybrid algorithms](https://mlsanity.com/paper/2211.15631/) (2022)
- [Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes](https://mlsanity.com/paper/2304.11247/) (2023)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation](https://mlsanity.com/paper/2211.08737/) (2022)
- [Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series](https://mlsanity.com/paper/2108.03190/) (2021)
- [Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble](https://mlsanity.com/paper/2401.07039/) (2024)
- [Power of Quantum Generative Learning](https://mlsanity.com/paper/2205.04730/) (2022)
- [Synthetic weather radar using hybrid quantum-classical machine learning](https://mlsanity.com/paper/2111.15605/) (2021)
- [Accelerating variational quantum algorithms with multiple quantum processors](https://mlsanity.com/paper/2106.12819/) (2021)
- [Building Continuous Quantum-Classical Bayesian Neural Networks for a Classical Clinical Dataset](https://mlsanity.com/paper/2406.06307/) (2024)
- [F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits](https://mlsanity.com/paper/2110.04253/) (2021)
- [Generalized quantum similarity learning](https://mlsanity.com/paper/2201.02310/) (2022)
- [Beyond Ans"atze: Learning Quantum Circuits as Unitary Operators](https://mlsanity.com/paper/2203.00601/) (2022)
- [Evaluating quantum generative models via imbalanced data classification benchmarks](https://mlsanity.com/paper/2308.10847/) (2023)
- [Quantum Algorithms: A New Frontier in Financial Crime Prevention](https://mlsanity.com/paper/2403.18322/) (2024)
- [Application of time-series quantum generative model to financial data](https://mlsanity.com/paper/2405.11795/) (2024)
- [A Hybrid Quantum Circuit Born Machine Framework for Financial Volatility Forecasting: Quantum-Assisted Training and Classical Inference](https://mlsanity.com/paper/2603.09789/) (2026)

## Abstract (arXiv)

Finding a concrete use case for quantum computers in the near term is still an open question, with machine learning typically touted as one of the first fields which will be impacted by quantum technologies. In this work, we investigate and compare the capabilities of quantum versus classical models for the task of generative modelling in machine learning. We use a real world financial dataset consisting of correlated currency pairs and compare two models in their ability to learn the resulting distribution - a restricted Boltzmann machine, and a quantum circuit Born machine. We provide extensive numerical results indicating that the simulated Born machine always at least matches the performance of the Boltzmann machine in this task, and demonstrates superior performance as the model scales. We perform experiments on both simulated and physical quantum chips using the Rigetti forest platform, and also are able to partially train the largest instance to date of a quantum circuit Born machine on quantum hardware. Finally, by studying the entanglement capacity of the training Born machines, we find that entanglement typically plays a role in the problem instances which demonstrate an advantage over the Boltzmann machine.