Speaker
Description
High-dimensional, sparse datasets capturing continuous biological processes, such as the cell cycle, are fundamental to understanding disease progression, such as cancer [1]. However, recovering these cyclic structures from highly stochastic data severely challenges classical machine learning. Standard metrics like Euclidean distance measure linear paths between data points; in noisy spaces failing to capture the true underlying shape [2], failing to distinguish genuine periodic signals from structural artefacts.
To overcome this, we introduce "Q-Cycle," a hybrid quantum-classical pipeline utilising quantum expressivity for robust shape recovery. Q-Cycle maps classical features into a quantum Hilbert space by encoding data into a parameterised quantum circuit via Chebyshev polynomials. This unrolls data through a non-linear frequency spectrum, acting as a geometric filter that stretches the intrinsic cyclic structure while naturally suppressing background noise.
Unlike standard quantum kernel methods reliant on supervised classification, Q-Cycle is fully unsupervised. To mitigate barren plateaus, it evaluates local Pauli observables to construct a stable, projected quantum similarity matrix. These noise-resilient affinities pass directly into a computational topology pipeline, explicitly extracting the global continuous loops of the underlying system.
Benchmarked against empirical datasets, Q-Cycle isolates sequential states and preserves macro-scale cyclic structures across severe noise thresholds where classical metrics degrade. This establishes a pathway towards demonstrating quantum advantage in high-dimensional representation learning.
References
[1] Oren, Y., et al. (2021). Nature, 596(7873), 576-582.
[2] Chari, T., & Pachter, L. (2023). PLoS Comput. Biol., 19(8), e1011288.
| Topic | Quantum kernel methods and their applications |
|---|---|
| Additional Topic | Hybrid quantum-classical approaches for learning and optimization |