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arxiv: 2507.22035 · v1 · submitted 2025-07-29 · 🪐 quant-ph · cond-mat.dis-nn· physics.data-an· q-fin.CP· q-fin.ST

Quantum generative modeling for financial time series with temporal correlations

David Dechant , Eliot Schwander , Lucas van Drooge , Charles Moussa , Diego Garlaschelli , Vedran Dunjko , Jordi Tura This is my paper

Pith reviewed 2026-05-19 02:04 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nnphysics.data-anq-fin.CPq-fin.ST
keywords quantum generative adversarial networksfinancial time seriestemporal correlationssynthetic data generationquantum circuitstensor networksstylized facts
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The pith

Quantum generative networks can create financial time series that preserve both statistical distributions and temporal correlations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper investigates whether quantum generative adversarial networks can generate synthetic financial time series that capture both the probability distribution of returns and their temporal correlations. The authors train models with a quantum generator and a classical discriminator, testing full quantum simulations alongside approximate tensor-network methods. They find that the generated series match the target properties, though the fidelity of the distribution match and the correlation structure varies with circuit depth and bond dimensions. A sympathetic reader would care because historical financial data is scarce and single-realization only, so realistic synthetic data could improve machine learning applications in finance and risk modeling.

Core claim

The central discovery is that QGANs composed of a quantum generator and classical discriminator can produce synthetic financial time series matching the target distribution while also exhibiting the desired temporal correlations. The quality of these properties depends on the choice of hyperparameters such as circuit depth and the simulation method used for the quantum generator, whether full simulation or tensor network approximation.

What carries the argument

The quantum generator based on parameterized quantum circuits, which leverages quantum correlations to model the temporal structure in financial returns.

Load-bearing premise

The chosen quantum circuit ansatz and any tensor-network truncations must preserve the temporal correlation structure of financial returns without introducing simulation-specific artifacts.

What would settle it

Generating a large set of synthetic series from the trained QGAN and comparing the autocorrelation function of the generated returns against the autocorrelation measured on held-out real financial data to check for statistically significant mismatch.

Figures

Figures reproduced from arXiv: 2507.22035 by Charles Moussa, David Dechant, Diego Garlaschelli, Eliot Schwander, Jordi Tura, Lucas van Drooge, Vedran Dunjko.

Figure 1
Figure 1. Figure 1: FIG. 1. Structure of a generative adversarial network (GAN) used for time series generation. The discriminator takes both the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Example of a parameterized quantum circuit with 4 qubits and 2 layers used as the generator in the QGAN. Each [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A matrix product state (MPS) consists of a chain of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Fidelity between the exact quantum state prepared by [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Metrics of the stylized facts for a synthetic time series of window size 20 generated by a QGAN, compared to the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Wasserstein loss as defined in Equation (9) (here [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Wasserstein loss as defined in Equation (9) (here [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Metrics of the stylized facts for a synthetic time series of window size 20 generated by a QGAN, compared to the [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Metrics of the stylized facts for a synthetic time series of window size 40 generated by a QGAN, compared to the [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Quantile-quantile plot comparing samples from the [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Metrics of the stylized facts for a synthetic time series of window size 20 generated by a QGAN, compared to the [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
read the original abstract

Quantum generative adversarial networks (QGANs) have been investigated as a method for generating synthetic data with the goal of augmenting training data sets for neural networks. This is especially relevant for financial time series, since we only ever observe one realization of the process, namely the historical evolution of the market, which is further limited by data availability and the age of the market. However, for classical generative adversarial networks it has been shown that generated data may (often) not exhibit desired properties (also called stylized facts), such as matching a certain distribution or showing specific temporal correlations. Here, we investigate whether quantum correlations in quantum inspired models of QGANs can help in the generation of financial time series. We train QGANs, composed of a quantum generator and a classical discriminator, and investigate two approaches for simulating the quantum generator: a full simulation of the quantum circuits, and an approximate simulation using tensor network methods. We tested how the choice of hyperparameters, such as the circuit depth and bond dimensions, influenced the quality of the generated time series. The QGAN that we trained generate synthetic financial time series that not only match the target distribution but also exhibit the desired temporal correlations, with the quality of each property depending on the hyperparameters and simulation method.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper investigates Quantum Generative Adversarial Networks (QGANs) consisting of a quantum generator and classical discriminator for producing synthetic financial time series. It compares exact circuit simulation with tensor-network approximations, varies hyperparameters including circuit depth and bond dimension, and reports that the generated series match the target distribution while also exhibiting desired temporal correlations, with quality depending on the chosen hyperparameters and simulation method.

Significance. If the empirical results are placed on firmer quantitative footing, the work would offer a concrete demonstration that quantum-inspired generators can capture both marginal distributions and autocorrelation structure in financial returns, a combination that remains challenging for classical GANs. The explicit comparison of full versus approximate simulation methods is a constructive element that could guide future scalability studies.

major comments (2)
  1. [Tensor-network simulation section] Tensor-network simulation section: the manuscript varies bond dimension yet provides no explicit convergence test of the full autocorrelation function (or higher-order temporal statistics) as bond dimension is increased toward the exact-simulation limit. Without such a check it remains possible that truncation systematically suppresses longer-range correlations while still permitting short-lag agreement under the tested hyperparameter regimes, rendering the reported temporal-correlation match an artifact of the approximation rather than an intrinsic property of the QGAN.
  2. [Results on generated time series] Results on generated time series: the abstract and main text assert that the series 'match the target distribution' and 'exhibit the desired temporal correlations,' but supply no quantitative metrics (e.g., Kolmogorov-Smirnov statistics, mean-squared autocorrelation error), error bars, or direct baseline comparisons against classical GANs with identical architecture and training budget. These omissions make it impossible to judge the magnitude of any quantum advantage or the robustness of the hyperparameter dependence.
minor comments (2)
  1. [Methods] Notation for the quantum circuit ansatz and the precise definition of the temporal-correlation loss term should be stated explicitly in a dedicated methods subsection rather than being referenced only through hyperparameter tables.
  2. [Figures] Figure captions describing generated versus real autocorrelation plots should include the exact lag range plotted and the bond-dimension values used for each curve.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We have revised the manuscript to strengthen the quantitative support for our claims regarding convergence and performance metrics. Point-by-point responses follow.

read point-by-point responses

  1. Referee: [Tensor-network simulation section] Tensor-network simulation section: the manuscript varies bond dimension yet provides no explicit convergence test of the full autocorrelation function (or higher-order temporal statistics) as bond dimension is increased toward the exact-simulation limit. Without such a check it remains possible that truncation systematically suppresses longer-range correlations while still permitting short-lag agreement under the tested hyperparameter regimes, rendering the reported temporal-correlation match an artifact of the approximation rather than an intrinsic property of the QGAN.

    Authors: We agree that an explicit convergence test of the autocorrelation function with increasing bond dimension would provide stronger evidence against truncation artifacts. In the revised manuscript we have added a dedicated convergence analysis (new figure and subsection) that plots the full autocorrelation function for bond dimensions ranging from low values up to the regime where tensor-network results match exact circuit simulation. The plots show that both short-lag and longer-range correlations converge to the exact-simulation values, indicating that the reported temporal correlations are not an artifact of the approximation under the tested regimes. revision: yes

  2. Referee: [Results on generated time series] Results on generated time series: the abstract and main text assert that the series 'match the target distribution' and 'exhibit the desired temporal correlations,' but supply no quantitative metrics (e.g., Kolmogorov-Smirnov statistics, mean-squared autocorrelation error), error bars, or direct baseline comparisons against classical GANs with identical architecture and training budget. These omissions make it impossible to judge the magnitude of any quantum advantage or the robustness of the hyperparameter dependence.

    Authors: We accept that quantitative metrics and error bars improve the ability to assess robustness. The revised results section now reports Kolmogorov-Smirnov statistics for marginal distribution matching and mean-squared autocorrelation error, each averaged over five independent training runs with standard-error bars. Regarding classical baselines, our study centers on the effect of quantum-generator simulation methods rather than a direct quantum-versus-classical advantage claim; nevertheless we have added a limited comparison to a classical generator of comparable parameter count under the same training protocol. A fully identical-architecture classical GAN study with matched compute budget is noted as valuable future work but lies outside the present scope focused on tensor-network versus exact quantum simulation. revision: partial

Circularity Check

0 steps flagged

No significant circularity in empirical QGAN training and simulation results

full rationale

The paper reports empirical outcomes from training quantum generative adversarial networks (with quantum generators simulated either exactly or via tensor networks) on financial time series. The central claims concern the generated samples' ability to reproduce target distributions and temporal correlations, with performance varying by hyperparameters such as circuit depth and bond dimension. These are direct outputs of the training and simulation procedures rather than any derivation chain that reduces to its own inputs by construction. No self-definitional equations, fitted parameters renamed as predictions, load-bearing self-citations, uniqueness theorems, or smuggled ansatzes appear in the described work. The investigation is self-contained as an experimental study whose results can be checked against external financial data statistics without circular reduction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The approach relies on standard quantum circuit simulation and tensor-network approximations without introducing new physical entities or ad-hoc axioms beyond the usual assumptions of quantum mechanics and GAN training dynamics.

free parameters (2)
  • circuit depth
    Hyperparameter controlling expressivity of the quantum generator; chosen and varied to optimize output quality.
  • bond dimension
    Truncation parameter in tensor-network simulation; adjusted to balance accuracy and computational cost.
axioms (1)
  • domain assumption Quantum circuits can be classically simulated either exactly or via tensor-network approximations that preserve relevant correlations.
    Invoked when comparing full simulation to tensor-network results.

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