Marco Paini (Rigetti Computing), Antoine Jacquier (Imperial College London), Michael Brett (Amazon Web Services), and collaborators from National Tsing Hua University and Standard Chartered demonstrated the feasibility of predicting financial market mid-prices using quantum enhanced signature kernels on Amazon Braket. Utilizing the SV1 state-vector simulator, the team performed exact simulations of 32-qubit circuits to analyze Limit Order Book (LOB) data, building upon an Innovate UK grant for Quantum Machine Learning (QML) development. This work validates the potential of incorporating quantum transformations into classical ML pipelines, offering a pathway toward improved financial forecasting capabilities despite current limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware.
Quantum Enhanced Signature Kernels for Financial Prediction
Researchers are exploring “Quantum Enhanced Signature Kernels” to improve financial prediction accuracy, specifically using Limit Order Book (LOB) data. This approach combines the power of signature kernels – effective for capturing time-series data – with quantum feature maps. Experiments, simulated on Amazon Braket’s SV1, utilized the publicly available FI-2010 dataset, predicting mid-price movements 10 ticks ahead with a classification model. The core idea is that quantum feature maps can enhance the performance of machine learning algorithms by better representing complex market dynamics.
The team reduced the dimensionality of the LOB data (originally 40 features) to 12, 16, 24, and 32 to manage computational demands while maintaining performance. Crucially, they focused on creating “high-magic” quantum feature maps—circuits generating output states with high stabilizer norms—believed to be particularly beneficial for machine learning. This contrasts with standard quantum feature maps like random Fourier features. The goal is to achieve a better approximation-generalization trade-off, potentially surpassing classical methods with limited data.
This work leverages the benefits of signature kernels—which efficiently represent path information—by pairing them with quantum transformations. Simulating up to 34 qubits on Amazon Braket’s SV1 allowed validation of the method without the noise present in current NISQ hardware. Early findings suggest that these quantum-enhanced signature kernels may offer a path toward more accurate and robust financial predictions, particularly in high-frequency trading scenarios where capturing subtle market changes is crucial.
Collaborative Research and Background
Collaborative research between Imperial College London, Rigetti Computing, Standard Chartered, and AWS has yielded promising results in applying quantum machine learning (QML) to financial data. Leveraging an Innovate UK grant and access to Amazon Braket’s SV1 simulator (capable of simulating up to 34 qubits), the team focused on predicting mid-price movements using Limit Order Book (LOB) data. This complex task—dealing with high-dimensional, rapidly changing market data—serves as a strong benchmark for evaluating QML algorithms against established classical methods.
The core of the approach lies in “quantum enhanced signature kernels.” These kernels utilize path signatures—a method for capturing the essential information from data streams—combined with quantum feature maps. Experiments using the publicly available FI-2010 dataset (containing 10 days of LOB data for 5 stocks) demonstrated potential improvements over classical methods. Researchers reduced the dataset’s 40 initial features to 12, 16, 24, and 32 to manage computational load, focusing on 1,000 training and 1,000 testing points.
A key innovation is the use of “high-magic” unitary transformations within the quantum feature map. This focuses on maximizing the ‘magic’—or non-classicality—of the resulting quantum state, a property theorized to enhance ML performance. By combining this with signature kernels, the team aims to achieve a better approximation-generalization tradeoff, potentially enabling superior performance even with limited training data—a crucial advantage in dynamic financial markets.
Amazon Braket and Simulation Resources
Amazon Braket’s SV1 state-vector simulator played a crucial role in testing quantum-enhanced signature kernels for financial prediction. Researchers leveraged the simulator to perform exact simulations with up to 34 qubits – a scale exceeding what’s currently feasible on noisy quantum hardware. This allowed validation of a machine learning approach using Limit Order Book (LOB) data – specifically predicting mid-price movements – without the distortions caused by quantum decoherence. The team utilized the publicly available FI-2010 dataset, a benchmark for market microstructure modeling.
This work focuses on improving kernel-based machine learning using “quantum feature maps” before applying signature kernels. Empirical evidence suggests these quantum transformations, built with ‘high-magic’ unitary transformations, can outperform classical methods. Experiments reduced the input feature count from the raw LOB data (40 features) to 12, 16, 24 and 32 to manage computational demands, while maintaining model performance. This approach aims to achieve a better approximation-generalization tradeoff in prediction.
The research highlights the potential of combining rough path theory – leveraging path signatures for data analysis – with quantum computing. While signature feature maps can be computationally expensive, efficient kernel tricks are used to address this. Amazon Braket’s SV1 simulator enabled rigorous testing of these quantum-enhanced signatures, providing a pathway towards more accurate financial predictions and showcasing a promising application of near-term quantum technologies.
Limit Order Book Data and Use Case
Limit Order Book (LOB) data—essentially lists of price and volume for buy/sell orders—forms the foundation for predicting market movements. High-frequency trading and complex market dynamics necessitate efficient methods to capture this data, which is often high-dimensional and rapidly changing. Researchers are leveraging the FI-2010 dataset—a publicly available benchmark with 10 days of data for 5 stocks—to test predictive models, specifically aiming to forecast mid-price movements 10 ticks ahead using 40 initial features.
A key innovation explored is the use of “signature kernels” – a method leveraging rough path theory to capture the order of events within the LOB data. Traditional signature calculations can become computationally expensive with high-dimensional data, but efficient kernel “tricks” have emerged. This work combines signature kernels with quantum feature maps—transformations applied to the data before signature calculation—hypothesizing these quantum enhancements can improve model performance beyond classical methods.
Experiments utilize Amazon Braket’s SV1 simulator to test models with up to 34 qubits. By reducing the initial feature set to 12, 16, 24, and 32, researchers balanced computational demands with predictive accuracy. The focus isn’t just on what the models predict, but on demonstrating that quantum machine learning (QML) algorithms offer a better trade-off between approximation and generalization, potentially outperforming classical ML when trained on limited data.
FI-2010 Dataset for Mid-Price Prediction
The FI-2010 dataset is a publicly available benchmark for financial market microstructure research, specifically Limit Order Book (LOB) data. It comprises 10 days of trading information for five stocks on the NASDAQ OMX Nordic exchange. Researchers utilize this dataset – containing roughly 200,000 training and 60,000 testing points – to develop and evaluate models predicting mid-price movements. Its accessibility makes it ideal for comparing performance of both classical and emerging Quantum Machine Learning (QML) algorithms in a controlled environment.
Recent work leverages FI-2010 to test Quantum Enhanced Signature Kernels, a method combining path signatures with quantum feature maps. Experiments focus on predicting mid-price shifts 10 ‘ticks’ ahead, framing the problem as a three-class classification (up, down, stationary). Dimensionality reduction, truncating the 40 original features to 12, 16, 24, or 32, was explored with minimal performance impact. This allows scaling experiments on quantum simulators like Amazon Braket’s SV1.
The core innovation lies in utilizing “high-magic” quantum circuits as feature maps before calculating path signatures. This approach aims to improve ML performance by leveraging quantum properties. Researchers hypothesize this boosts the approximation-generalization tradeoff, potentially surpassing classical methods, especially with limited training data – a key observation from prior discrete logarithm problem research. The FI-2010 dataset provides a vital testing ground for verifying this potential.
Problem Formulation and Benchmark Models
Problem formulation centers on predicting mid-price movements in Limit Order Book (LOB) data, a crucial task for market making and execution. Researchers utilized the publicly available FI-2010 dataset – comprising 10 days of data for 5 stocks – modeling the prediction as a multi-class classification problem. This involved forecasting price movements (up, down, or stationary) 10 ticks ahead, using 40 features derived from the LOB. Strong classical benchmarks, like the DeepLOB model, were established for comparative analysis, using training sets of ~200,000 points and testing on ~60,000.
A core challenge addressed was the exponential growth of features when using signature kernels – a method for capturing path information in data streams. To mitigate this, experiments reduced the input feature count from the full 40 to 12, 16, 24, and 32, assessing the impact on model performance. This dimensionality reduction, truncating the number of LOB pairs, allowed for practical simulation on the Amazon Braket SV1 simulator, enabling exact simulations of up to 34 qubits—essential for validating quantum machine learning (QML) potential without noise.
Researchers hypothesized that QML algorithms could achieve a superior approximation-generalization tradeoff compared to classical methods, particularly with limited data. They focused on combining signature kernels with quantum feature maps, leveraging the ‘magic’ of the resulting quantum state—a measure of its non-classicality. Initial findings, presented at IEEE Quantum Week 2024, suggest that these specific quantum feature maps outperform classical counterparts, potentially improving prediction accuracy in financial applications.
Quantum Experiment Setup and Data Reduction
Quantum experiments focused on financial data prediction leveraged Amazon Braket’s SV1 simulator to test quantum enhanced signature kernels – a technique using up to 32 qubits. Researchers aimed to predict mid-price movements in Limit Order Book (LOB) data, utilizing the publicly available FI-2010 dataset. This approach tackled the challenges of high-dimensional, rapidly changing financial data, seeking to improve prediction accuracy beyond classical machine learning methods. Reducing features from the initial 40 down to 12-32 allowed manageable circuit depths.
The core of the experiment revolved around “signature kernels,” a method derived from rough path theory, efficiently capturing the essential order of events within the LOB data stream. To boost performance, a quantum feature map was applied before calculating the signature. Rigetti Computing demonstrated that specific quantum feature maps outperform classical alternatives, potentially improving predictive power—especially with limited training data. The key lies in maximizing ‘magic’—a measure of a quantum state’s non-classicality—within the feature map circuit.
Researchers trained and tested models on subsets of the FI-2010 dataset (around 200,000 & 60,000 points respectively). The mid-price prediction was framed as a classification problem (up, down, or stationary – within 0.2 basis points). The use of simulation—while avoiding noise issues in current quantum hardware—was limited by exponential resource scaling with qubit count. This necessitated careful dimension reduction of the input features while preserving model performance.
Signature Kernels and Rough Path Theory
Signature kernels, rooted in rough path theory, offer a powerful approach to analyzing complex data streams like financial market data. This technique leverages “path signatures” – a hierarchical representation capturing the order of events – to create effective feature maps for machine learning. While traditionally computationally expensive due to exponential feature growth, recent advances in kernel tricks, developed at Imperial College London, allow efficient computation by connecting signatures to hyperbolic partial differential equations. This unlocks the potential of infinitely many signature features without prohibitive costs.
Researchers are now exploring quantum enhanced signature kernels. Rigetti Computing has demonstrated that strategically designed quantum feature maps—transformations applied before signature calculation—can outperform classical alternatives. This improvement is linked to the “magic” of the resulting quantum state – a measure of its distance from easily simulatable states. Experiments utilizing Amazon Braket’s SV1 simulator, processing Limit Order Book data (like the FI-2010 dataset with 40+ features), aim to validate performance gains, even with limited training data (e.g., 1,000 points).
The core benefit lies in potentially improved generalization with fewer data points. Standard Chartered provided challenging, real-world market microstructure data for testing. Researchers reduced feature counts (to 12, 16, 24, or 32) to manage computational demands without significant performance loss. By predicting mid-price movements 10 ticks ahead using a multi-class classification (up, down, stationary), this work aims to show that quantum-enhanced signatures offer a superior approximation-generalization tradeoff compared to classical machine learning methods.
Quantum Feature Maps and Performance Gains
Quantum feature maps are showing promise in enhancing machine learning performance, particularly with complex financial data. Recent work utilizing Amazon Braket’s SV1 simulator tested quantum-enhanced signature kernels – a method leveraging path signatures as feature maps – on Limit Order Book (LOB) data to predict mid-price movements. Researchers achieved this with up to 32 qubits, demonstrating the potential of quantum transformations within classical ML pipelines. The core idea is to improve feature representation before applying the signature kernel.
This research focused on predicting mid-price movements 10 ticks ahead using the publicly available FI-2010 dataset – a benchmark for market microstructure models. By reducing the input features from the original 40 down to 12, 16, 24, or 32, the team could effectively simulate larger quantum circuits. Early results suggest these quantum feature maps outperform classical counterparts, potentially offering a better approximation-generalization tradeoff – a crucial aspect when working with limited data, as often seen in financial applications.
The effectiveness of these quantum feature maps stems from the ‘magic’ of the output state created by the quantum circuit. Specifically, circuits producing states with a high stabilizer norm seem to be most beneficial. This ‘magic’ allows for better feature representation, enhancing the downstream ML model’s performance. While current NISQ devices are noisy, exact simulations, like those enabled by Amazon Braket’s SV1, are crucial for validating the potential of these techniques before deployment on actual quantum hardware.
Measuring ‘Magic’ in Quantum Feature Maps
Researchers are actively quantifying the “magic” within quantum feature maps to understand why certain quantum circuits boost machine learning performance. ‘Magic’—specifically, the stabilizer norm of the output state—indicates how far a quantum state deviates from what classical computers can easily simulate. Higher ‘magic’ suggests a greater potential for quantum advantage. This work, utilizing Amazon Braket’s SV1 simulator with up to 34 qubits, focuses on applying these maps to financial time-series data—specifically, Limit Order Book (LOB) data—to predict mid-price movements.
The team tested quantum enhanced signature kernels—combining path signatures with quantum feature maps—using the publicly available FI-2010 dataset. They reduced the input feature count (from 40 to 12, 16, 24, and 32) while maintaining performance to manage computational complexity. The goal is to demonstrate improved approximation-generalization tradeoffs compared to classical methods, particularly when training with limited data—a common challenge in financial modeling. Preliminary results suggest promise, building on prior work predicting US recessions.
This research leverages a sophisticated kernel trick based on signature kernels, a method inspired by rough path theory. By measuring the ‘magic’ of the quantum feature map’s output state, researchers aim to pinpoint which quantum transformations offer the greatest advantage for machine learning tasks. This focus on quantifying ‘magic’ offers a critical lens for evaluating the potential of near-term quantum devices in complex financial applications, moving beyond simply showing improvement to understanding the underlying mechanisms.
