Eigenvalue and eigenspace anholonomies in hierarchical systems

TL;DR

This paper explores how recursive quantum circuits can exhibit eigenvalue and eigenspace anholonomies during adiabatic parameter cycles, revealing complex state evolutions beyond spectral degeneracy.

Contribution

It demonstrates that large, recursively constructed quantum circuits can display eigenvalue and eigenspace anholonomies, extending the understanding of quantum adiabatic cycles.

Findings

Recursive quantum circuits can exhibit eigenvalue anholonomies.

Eigenvalue and eigenspace anholonomies occur without spectral degeneracy.

An arbitrarily large circuit can show these exotic adiabatic effects.

Abstract

An adiabatic cycle of parameters in a quantum system can yield the quantum anholonomies, nontrivial evolution not just in phase of the states, but also in eigenvalues and eigenstates. Such exotic anholonomies imply that an adiabatic cycle rearranges eigenstates even without spectral degeneracy. We show that an arbitrarily large quantum circuit generated by recursive extension can also exhibit the eigenvalue and eigenspace anholonomies.