Quantum Reservoir Computing and Risk Bounds
This work addresses the need for theoretical guarantees in quantum machine learning, particularly for quantum reservoir computing, but it is incremental as it extends classical complexity methods to a quantum context.
The paper tackles the problem of bounding generalization errors in quantum reservoir computing by using Rademacher complexity, providing specific parameter-dependent bounds for two quantum reservoir classes and showing that risk bounds converge with training samples, though they scale exponentially with the number of qubits.
We propose a way to bound the generalisation errors of several classes of quantum reservoirs using the Rademacher complexity. We give specific, parameter-dependent bounds for two particular quantum reservoir classes. We analyse how the generalisation bounds scale with growing numbers of qubits. Applying our results to classes with polynomial readout functions, we find that the risk bounds converge in the number of training samples. The explicit dependence on the quantum reservoir and readout parameters in our bounds can be used to control the generalisation error to a certain extent. It should be noted that the bounds scale exponentially with the number of qubits $n$. The upper bounds on the Rademacher complexity can be applied to other reservoir classes that fulfill a few hypotheses on the quantum dynamics and the readout function.