Conceptos Básicos
Post-variational quantum neural networks exchange the expressibility of parameterized quantum circuits with trainability of the entire model, providing a guarantee of finding a global minimum over a constructed convex optimization landscape.
Resumen
The content discusses post-variational strategies as an alternative to variational quantum algorithms for machine learning tasks. The key ideas are:
Variational quantum algorithms face challenges like barren plateaus, causing difficulties in gradient-based optimization.
Post-variational strategies replace parameterized quantum circuits with fixed quantum circuits, and find the optimal combination of these circuits through classical convex optimization.
Two main heuristic strategies are proposed to construct post-variational quantum circuits:
Ansatz expansion: Expand the variational Ansatz into an ensemble of fixed Ansätze using Taylor series.
Observable construction: Directly decompose the parameterized observable into a linear combination of fixed observables (e.g. Pauli observables).
A hybrid approach combines both strategies.
The post-variational quantum neural network architecture mimics a two-layer classical neural network, with the fixed quantum circuits as the first layer and a classical linear regression model as the second layer.
Error analysis shows that the post-variational approach can achieve a target loss within ε by using a number of quantum measurements that scales polynomially in the problem parameters, in contrast to the potential exponential scaling of variational algorithms.
The post-variational approach provides a guarantee of finding the global minimum over the constructed convex optimization landscape, unlike variational algorithms which may get stuck in local minima.