An ergodic abelian skeleton for quantum systems

Julian Boesl, Yu-Jie Liu, Frank Pollmann +1 more

We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite correlation length deformations of string-net fixed points, which are constructed both by conserving virtual symmetries of the tensor and by imposing local isometry constraints. They connect distinct topological phases via a shared critical point, thereby providing analytically tractable examples of phase transitions beyond anyon condensation. By mapping such classes of 2D tensor networks to 1D stochastic automata with local update rules, we show that expectation values of generalized Pauli strings of arbitrary weight can be efficiently computed using classical methods. Therefore these skeletons not only serve as an organizing principle for abelian topological order but also provide a non-trivial testbed for quantum processors.

Th.J. Siskens, Peter Bongaarts

Pragya Shukla

Abstract The presence of local interactions and wave-localization phenomena is quite generic to a wide range of complex systems. Based on the evidence of two transitions similar to those in many body states as well as single particle states, the work by Kravtsov et al (2015 New J. Phys. 17 122002 ) indicates the strong prospect of Rosenzweig–Porter ensemble to serve as the good model for many particle localization as well as that of single particle. With already well-known statistical universality of ergodic dynamics, this also reveals the next level in the hierarchy of the universality of statistical fluctuations.

Th.J. Siskens, Peter Bongaarts

Lon Van Hove

Andrew Stewart Caldin

Driving the E8 root system at its 10800th harmonic (132 Hz × 10800 = 1,425,600 Hz) with a phi‑modulated Floquet field resonantly locks the 5‑skeleton of the Gosset 4_21 polytope, imposing Fibonacci parafermion zero‑mode networks on each 5‑cell (4‑simplex) of the lattice. The phi coupling creates a self‑similar hierarchy that extends the previously observed 2‑, 3‑, and 4‑skeleton lockings into a fully connected, non‑Abelian anyonic fabric spanning all 240 root vectors. This universal parafermion braiding enables topologically protected quantum gates directly from the E8 geometry, providing a pathway to fault‑tolerant quantum computation rooted in exceptional Lie symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com