Speaker
Description
This extended abstract summarises the full paper "Circuit Harmonic Matrices: A Spectral Framework for Quantum Machine Learning". Parametrised quantum circuits are central to near-term QML, but architectural choices such as encoder, ansatz, entangling pattern, observable, and input state are often difficult to assess before training. We introduce the circuit harmonic matrix $C$, a data-independent spectral object for quantum Fourier models with commuting phase encoders and Pauli-rotation trainable blocks. $C$ maps parameter harmonics to input harmonics, making explicit which learnable Fourier modes are supported by the same trainable degrees of freedom.
We show that coefficient variances, frequency-frequency covariances, correlations, and the quantum neural tangent kernel are quadratic forms in $C$. This yields a pre-training diagnostic of spectral bias, mode coupling, and reachable tangent directions, separating architecture-dependent structure from dataset projection and optimisation trajectory. We also give a constructive Heisenberg-picture Pauli-propagation interpretation of $C$, and validate the resulting covariance and correlation predictions against independent Monte Carlo estimates.
The framework provides an analytical basis for comparing, selecting, and designing PQC architectures while also making explicit the effect of ansatz choice on learning capability.
| Topic | Theoretical foundations of quantum learning |
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