Enhanced fill probability estimates in institutional algorithmic bond trading using statistical learning algorithms with quantum computers (2509.17715v1)

Abstract: The estimation of fill probabilities for trade orders represents a key ingredient in the optimization of algorithmic trading strategies. It is bound by the complex dynamics of financial markets with inherent uncertainties, and the limitations of models aiming to learn from multivariate financial time series that often exhibit stochastic properties with hidden temporal patterns. In this paper, we focus on algorithmic responses to trade inquiries in the corporate bond market and investigate fill probability estimation errors of common machine learning models when given real production-scale intraday trade event data, transformed by a quantum algorithm running on IBM Heron processors, as well as on noiseless quantum simulators for comparison. We introduce a framework to embed these quantum-generated data transforms as a decoupled offline component that can be selectively queried by models in low-latency institutional trade optimization settings. A trade execution backtesting method is employed to evaluate the fill prediction performance of these models in relation to their input data. We observe a relative gain of up to ~ 34% in out-of-sample test scores for those models with access to quantum hardware-transformed data over those using the original trading data or transforms by noiseless quantum simulation. These empirical results suggest that the inherent noise in current quantum hardware contributes to this effect and motivates further studies. Our work demonstrates the emerging potential of quantum computing as a complementary explorative tool in quantitative finance and encourages applied industry research towards practical applications in trading.

• The paper demonstrates that quantum-generated features can improve fill probability estimation, achieving up to a 34% relative gain over classical methods.
• It introduces a two-stage mapping via a Projected Quantum Feature Map on IBM Heron 109-qubit processors, validated on a production-scale European bond trading dataset.
• Quantum hardware noise is shown to act as a regularizer, leading to smoother feature distributions and robust enhancements in model performance.

Enhanced Fill Probability Estimation in Algorithmic Bond Trading via Quantum-Generated Features

Introduction

This paper presents an empirical investigation into the use of quantum computing for enhancing fill probability estimation in institutional algorithmic bond trading. The focus is on the European corporate bond market, where the estimation of the likelihood that a trade order (specifically, a response to a Request for Quote, RFQ) will be filled is a central component of algorithmic trading strategies. The authors propose a framework in which quantum computers are used to generate feature transformations of classical trading data, which are then used as inputs to standard machine learning models for fill probability estimation. The paper benchmarks the performance of models trained on quantum-transformed features against those trained on classical features and features generated by noiseless quantum simulation.

Problem Formulation and Motivation

The fill probability estimation problem is characterized by two fundamental sources of uncertainty: (1) the irreversibility and non-stationarity of financial time series, and (2) the partial observability and high dimensionality of market state representations. In the context of corporate bond trading, the challenge is exacerbated by sparse pricing data, high-dimensional feature spaces, and the stochastic, non-linear interactions inherent in market microstructure.

The authors formalize the problem as learning a function $\tilde{\Lambda}: \mathbb{R}^p \rightarrow [0,1]$ that maps a market state representation $x$ (a vector of $p$ features) to the probability that a given RFQ response will be filled. The key innovation is to decouple the feature engineering process from the learning process by introducing a quantum-generated feature transformation $\phi: \mathbb{R}^p \rightarrow \mathbb{R}^q$, resulting in a two-stage mapping $x \xrightarrow{\phi} x' \xrightarrow{g} P(y=1|x')$.

Quantum Feature Generation Methodology

The quantum feature generation is implemented via a Projected Quantum Feature Map (PQFM). The process consists of:

1. Quantum Embedding: Each classical feature vector $x$ is encoded into a quantum state $|\psi_{x,\alpha}\rangle$ using a parameterized quantum circuit based on a Heisenberg ansatz. The circuit operates on $N$ qubits, with the classical features mapped to the coupling parameters of the Heisenberg Hamiltonian, and the circuit depth controlled by the number of Trotter steps.
2. Measurement: A set of $q$ Pauli observables (typically all single-qubit $X$, $Y$, $Z$ operators) are measured on the quantum state, and the expectation values are used as the transformed feature vector $x' \in \mathbb{R}^q$.
3. Implementation: The PQFM is executed both on IBM Heron quantum hardware (with 109 qubits) and on noiseless quantum simulators. Error mitigation techniques such as Pauli Twirling and TREX are applied to hardware runs.

The transformation is strictly a function of the input data and is independent of the outcome labels, ensuring that any observed improvements in model performance are attributable to the feature transformation itself.

Empirical Analysis and Backtesting Protocol

The empirical paper uses a production-scale dataset from HSBC, covering 294 trading days and over 1 million RFQs. The active analysis window comprises 69 trading days, with 143,912 RFQs and 216-dimensional feature vectors per event. The dataset is preprocessed and normalized before quantum transformation.

A rigorous backtesting protocol is employed:

• For each test instance, models are trained on a rolling window of past events, with varying "blinding" windows (i.e., the time gap between training and test data).
• Four model classes are evaluated: Logistic Regression (LR), Random Forest (RF), Gradient Boosting (XGB), and Feed-Forward Neural Network (NN).
• The primary evaluation metric is the area under the ROC curve (AUC), which is robust to class imbalance and threshold selection.

Quantum-generated features are compared against classical features and features generated by noiseless quantum simulation. Additionally, a classical-quantum event matching (CQEM) protocol is introduced to enable the reuse of quantum-generated features for unseen but similar classical events, further decoupling the feature transformation from the outcome labels.

Results

Feature Distribution Analysis

Quantum-generated features exhibit smoother, more normal-like distributions compared to the complex, multi-modal distributions of classical features. The degree of smoothing increases with circuit depth and hardware noise, suggesting that quantum noise acts as a regularizer on the feature space.

Model Performance

• Classical Features: All models achieve a median test AUC of approximately 0.63, with no significant sensitivity to the blinding window.
• Noiseless Quantum Simulation: Models trained on simulated quantum features perform slightly worse than those trained on classical features (median AUC $\sim$0.60).
• Quantum Hardware Features: Models trained on hardware-generated quantum features exhibit substantial performance gains. For the "shorter" circuit, median AUC increases to $\sim$0.75 (no blinding), while for the "longer" circuit, median AUC reaches $\sim$0.97, representing a relative gain of up to 34% over classical features. The performance decays with increasing blinding window but remains elevated compared to classical and simulated quantum features.

These gains are consistent across all model classes and are robust to variations in hardware (different IBM Heron devices) and circuit parameters. Notably, the performance uplift is not reproduced by simulated quantum features with artificially induced noise, indicating that the specific characteristics of hardware noise are critical.

Classical-Quantum Event Matching

The CQEM protocol demonstrates that quantum-generated features can be effectively reused for unseen events with similar classical representations, maintaining high model performance (AUC $\sim$0.89 at 97% matching resolution). This further supports the hypothesis that quantum hardware noise introduces beneficial structure into the feature space.

Analysis of Quantum Hardware Noise

Experiments indicate that quantum hardware noise induces small but measurable drifts in the PQFM features over time. However, these drifts do not fully explain the observed performance gains, and the precise mechanism by which hardware noise enhances model performance remains an open question.

Implementation Considerations

Resource Requirements

• Quantum Hardware: The experiments utilize 109-qubit circuits on IBM Heron processors, with 4096 measurement shots per observable. Circuit depth and noise characteristics are critical parameters.
• Classical Infrastructure: Preprocessing, model training, and backtesting are performed on standard compute clusters using Python, scikit-learn, and XGBoost.

Integration Strategy

• The quantum feature generation is implemented as an offline, decoupled component. Transformed features are stored and selectively queried by the online trading system, ensuring low-latency inference.
• The approach is model-agnostic: any downstream statistical learning algorithm can be used without modification.

Limitations

• The observed performance gains are data-instance specific and lack theoretical generalization guarantees.
• The beneficial effect of quantum hardware noise is not theoretically understood and may not generalize to other datasets or market environments.
• The approach is currently limited by the scale and noise characteristics of available quantum hardware.

Implications and Future Directions

The empirical results suggest that quantum hardware, even in the presence of significant noise, can generate feature transformations that enhance the learnability of complex, high-dimensional financial time series. This effect is not reproduced by noiseless simulation or classical feature engineering, indicating a unique role for quantum noise in regularizing or enriching the feature space.

From a practical perspective, the framework enables the integration of quantum-generated features into existing algorithmic trading pipelines without increasing model complexity or violating regulatory constraints on model risk management. The decoupled, offline nature of the quantum transformation is compatible with the latency requirements of institutional trading systems.

Theoretically, the findings raise important questions about the role of quantum noise in statistical learning and the potential for quantum devices to act as generative regularizers for complex data distributions. Further research is needed to elucidate the mechanisms underlying the observed performance gains and to explore the generalizability of the approach to other domains and datasets.

Conclusion

This paper demonstrates that quantum computers, even in their current noisy intermediate-scale quantum (NISQ) incarnation, can serve as effective tools for generating feature transformations that enhance the performance of statistical learning models in algorithmic trading. The empirical evidence of substantial out-of-sample performance gains, attributable to quantum hardware noise, motivates further investigation into the intersection of quantum information processing and financial machine learning. The proposed framework provides a practical pathway for the integration of quantum computing into real-world trading systems and highlights the need for continued research into the theoretical foundations and broader applicability of quantum-enhanced statistical learning.