Quantum theory and photonic systems pave way towards scalable quantum learning machines
Quantum computing continues to challenge conventional thinking with its promise of solving complex problems more efficiently than classical systems.
Two recent studies from EQUS Chief Investigator A/Prof Sally Shrapnel’s team at UQ present significant progress towards applying quantum machine learning to future global challenges.
The first paper, led by Cassie Bowie, investigated how a particular quantum phenomenon known as Hong–Ou–Mandel interference can provide a physical platform for more efficient quantum kernel evaluations.
Meanwhile the second paper, led by Dr Laura Henderson (also at UQ), delves even deeper into the mathematical underpinnings, deriving analytic expressions for quantum kernels in infinite-dimensional systems to establish a rigorous taxonomy describing their classical computational equivalence.
Together, these studies offer fresh perspectives on how quantum resources could revolutionise kernel-based machine learning.
Kernel-based machine learning: Mapping data into higher dimensions
Classical machine learning is often energy-intensive, driven by computations performed across immense datasets.
Kernel-based learning is a mathematical approach used for classification and regression tasks, quantifying the similarity between data points, and mapping data onto high-dimensional spaces to make patterns linearly separable.
However, this mapping can be computationally expensive, especially for high dimensional (or even infinite-dimensional) spaces.
“This is where quantum mechanics plays a role” says Dr Michael Kewming, previously an EQUS Research Fellow in Sally’s group, “Leveraging principles such as superposition and entanglement allows information to be processed in unique ways, so quantum algorithms can solve problems much more efficiently than classical computers.”
Harnessing physical interference as a computational tool
Cassie Bowie’s study investigated how a particular quantum phenomenon can provide a physical platform for efficient quantum kernel evaluations.
Hong–Ou–Mandel interference is a quintessentially quantum phenomenon that allows one to measure and quantify the additional quantum degrees of freedom present within photons. In this effect, two photons entering a beam splitter will emerge together in the same output port when their quantum states are identical. However, any difference in state will proportionally reduce the probability of emerging through the same port.
“By harnessing the degrees of freedom in a photon, we can encode multi-dimensional data (theoretically, infinite-dimensional data) in a single photon, and the evaluation does not scale with complexity,” says Cassie, who is an EQUS PhD candidate.
Cassie demonstrated that the multi-dimensional data encoded into a single photon could simply be evaluated in a single(repeated) measurement.
While the published work demonstrates the effectiveness of this principle using the encoding of simple classical data, extending it to quantum data could further improve the efficiency of processing quantum kernels, leveraging proven advantages in quantum machine learning.
The work not only establishes a specific physical implementation for quantum kernels but also underscores the potential of photonic (light-based) platforms in quantum machine learning.
Building a taxonomy for continuous-variable quantum kernels
Building on these concepts, Laura Henderson’s paper tackles the challenge of understanding and generalising quantum kernels for continuous-variable (CV) systems, such as photonic platforms.
“The work provides a finitely-defined (i.e. ‘closed-form’) expression for quantum kernels in infinite-dimensional spaces,” says Laura, who is an EQUS Research Fellow.
Insights gained via closed form expression allow more intuitive tuning of the machine learning model’s initialisation parameters (called ‘hyperparameters’) and understanding of their computational advantages.
Laura’s study also offers a taxonomy for assessing the computational benefits of different methods of mapping data onto the quantum kernel in CV systems.
Additionally, by comparing quantum kernels with their classical counterparts, the research provides tools for identifying scenarios where CV quantum systems may exhibit exponential advantages and others where classical approaches might suffice.
This systematic approach highlights the importance of choosing the right quantum resources for specific machine learning tasks.
Bridging physics and machine learning, and the future of quantum kernels
The two studies represent complementary advances in the field. Cassie’s paper provides a tangible, experimentally realisable method for quantum kernel evaluation, while Laura’s work offers a theoretical foundation that can guide future research and practical applications.
Together, they bring us closer to realising the potential of quantum learning machines, focus of EQUS’ Quantum Engines and Instruments research program.
“Cassie’s work creates a new physical platform for quantum machine learning while Laura’s research develops a new framework for a whole family of quantum learning machines,” says Sally.
By exploring theoretical approaches with an emphasis on currently available experimental implementation, these papers showcase how quantum mechanics can offer practical benefits for machine learning, potentially transforming industries reliant on data analysis.
Photonic systems, with their reliance on quantum phenomena, offer a promising avenue for building practical quantum learning machines.
As quantum technologies advance, the methodologies outlined in these papers could pave the way for scalable and efficient machine learning models.
This story was first published in the 2024 EQUS annual report.