Speaker
Description
In this work, we analyze trainability from the perspective of observable orbits induced by parameterized quantum circuits (PQCs). We study how the number of independent data-visible tangent directions affects the conditioning of the quantum Fisher information matrix (QFIM) and the quantum neural tangent kernel (QNTK). Our main hypothesis is that trainability is determined not only by the total dimension of the dynamical Lie algebra, but also by how the ansatz generators sample tangent directions at finite depth and by how these directions are observed by the chosen observable, input state, and training data. Thus, two ansätze may generate the same dynamical Lie algebra while producing different finite-depth tangent spectra and, consequently, different QFIM or QNTK condition numbers.
Under this framework, we also analyze how increasing the number of layers either increases or concentrates this visibility by measuring the novelty contributed by each layer. Our results suggest that trainability is not controlled only by the dimension of the reachable Lie algebra, but by the spectral distribution of observable-visible tangent directions. In particular, circuits with richer ansatz generators can improve the condition number by adding independent directions that strengthen weak eigenmodes rather than concentrating tangent energy only in dominant directions.
| Topic | Quantum variational circuits and their applications |
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| Additional Topic | Theoretical foundations of quantum learning |