Classical Surrogates Enable Scalable Inference for Quantum Machine Learning Models

Quantum machine learning holds considerable promise for near-term industrial applications, but a lack of readily available quantum hardware currently restricts its widespread adoption. Philip Hernicht, Alona Sakhnenko, and Corey O’Meara, along with colleagues from E. ON Digital Technology and the Fraunhofer Institute for Cognitive Systems IKS, address this challenge by developing improved methods for creating classical surrogates, lightweight, classical representations of quantum models. The team reveals that existing techniques for generating these surrogates demand excessive computational resources, hindering scalability, and proposes a new pipeline that dramatically reduces this burden. By minimising redundancies in the process, they demonstrate the ability to create accurate classical surrogates using far fewer resources, and validate its effectiveness on a real-world energy demand forecasting problem, paving the way for faster integration of quantum-inspired solutions into practical industrial settings and accelerating research into demonstrable quantum advantage.

Quantum machine learning (QML) offers potential advantages for certain computational tasks, yet limited access to quantum hardware remains a significant bottleneck for deploying QML solutions. This work explores the use of classical surrogates to bypass this restriction, a technique that allows building a lightweight classical representation of a (trained) quantum model, enabling inference on entirely classical devices. The research reveals prohibitively high computational demand associated with previously proposed methods for generating classical surrogates from quantum models, and proposes an alternative pipeline enabling generation of classical surrogates at a larger scale than was previously possible.

Classical Surrogates for Quantum Kernel Methods

Researchers are developing methods for creating classical surrogates for Quantum Kernel Methods (QKMs), specifically Parameterized Quantum Circuits (PQCs). These surrogates replace the computationally expensive evaluation of quantum circuits with a much faster classical approximation, crucial for scaling QKMs to larger problems. The authors address the challenge of needing sufficient data to accurately train the surrogate by proposing solutions involving data augmentation. Quantum Kernel Methods utilize quantum circuits to define kernel functions, mapping data into a high-dimensional quantum feature space.

A classical surrogate is a classical model, in this case a kernel regression model, that approximates the behavior of the PQC, trained on data generated by evaluating the PQC. The surrogate aims to approximate the PQC’s kernel function, leveraging kernel theory and a technique called Random Fourier Features to achieve this. Random Fourier Features approximate kernel functions by randomly sampling frequencies. To improve surrogate performance, especially with limited data, the team employs data augmentation, generating synthetic data to increase the training dataset size. Results demonstrate that a classical surrogate can accurately approximate a PQC, provided enough data points are used for training.

They derived theoretical bounds on the number of frequency samples needed to guarantee a certain error between the quantum model and the surrogate, finding these bounds grow linearly with the dimensionality of the data. Using a Diffusion Model to generate synthetic data significantly improves surrogate performance, especially when the original dataset is limited, reducing relative MSE with the addition of 10,000 synthetic data points. The authors emphasize that the surrogate will fail if the training dataset is incomplete or does not adequately represent the underlying data distribution. Ultimately, creating classical surrogates for PQCs is a promising way to overcome the computational limitations of quantum machine learning, but the performance of the surrogate is highly dependent on the size and quality of the training dataset, making data augmentation essential.

Classical Surrogates Enable Quantum Model Inference

This work addresses a key challenge in quantum machine learning: the limited access to quantum hardware for deploying trained models. Researchers developed a method to create classical surrogates, lightweight classical representations of quantum models, enabling inference on standard computers. Previous approaches to generating these surrogates demanded substantial computational resources, even for relatively small models, hindering practical application. This new method significantly reduces these demands, scaling resource requirements linearly rather than exponentially. The team demonstrated its effectiveness by applying it to a real-world energy demand forecasting problem, achieving high accuracy in both simulations and on actual quantum hardware.

This advancement allows for the transformation of complex quantum models, which previously required terabytes of memory, into versions that can run on standard laptops, representing a substantial reduction in algorithmic space complexity. The authors acknowledge that further research should explore the connections between this surrogation technique and other methods for representing quantum models classically, such as shadow models and tensor networks. Investigating the limitations of these various approaches could reveal scenarios where efficiently representing quantum models classically becomes impossible, potentially highlighting opportunities for genuine quantum advantage. Ultimately, this work represents a significant step towards integrating quantum machine learning into practical applications, particularly in areas where real-time processing, security, or cost are critical concerns.