Speaker
Description
Quantum reservoirs (QRs) are a hardware-friendly route to quantum machine learning on near-term devices, but their performance depends critically on the choice of fixed reservoir dynamics. Existing diagnostics often rely on model-specific assumptions or require access to the full quantum state, unitary, or output distribution, limiting their scalability. We introduce a two-level diagnostic framework that separates intrinsic reservoir expressivity from task-dependent feature coverage.
First, we adapt order-statistics (ORS) to quantify how close a reservoir ensemble is to Haar-random behavior using only the top-$K$ output probabilities. The resulting expressivity gap
$G_{\mathrm{ORS},K}=\Lambda_K-\Lambda_{\mathrm{Haar},K}$
is scalable with Hilbert-space dimension, applies to arbitrary reservoir families, admits a depolarizing-noise correction, and can be extended across multiple local Pauli measurement bases to test basis-robust randomness. Second, we measure coverage through the effective rank of the centred feature matrix,
$R_{\mathrm{eff}}(H_c)=\frac{(\sum_i \sigma_i)^2}{\sum_i \sigma_i^2}$
which estimates how many independent feature directions are available to the classical readout.
We evaluate these diagnostics across random-gate and IQP-style reservoir families, comparing them with KL expressivity, level-spacing statistics, and Krylov complexity in regimes where those quantities are accessible. Across Quantum Extreme Learning Machine and Quantum Reservoir Computing benchmarks, including Fourier regression, LiH energy prediction, NARMA forecasting, and residential energy forecasting, good performance consistently arises when reservoirs are both expressive and high-coverage. These results position multi-basis ORS and effective rank as practical, scalable design tools for selecting QRs that are expressive, task-suitable, and compatible with noisy hardware.
| Topic | Quantum algorithms for machine learning applications |
|---|---|
| Additional Topic | Theoretical foundations of quantum learning |