Rewire and reset are all you need: Minimal resources for manipulating non-Abelions
Abstract
Braiding and fusing anyons are fundamental to topological quantum computation, yet existing circuit protocols often employ ancillas and measurements. We determine the minimal circuit resources for performing such anyon operations in quantum double models of generic finite groups. Our approach braids anyons through a sequential unitary circuit without ancillas. Intuitively, this is obtained by deforming the underlying graph on which the anyons live. More generally, we introduce graph rewiring, a diagrammatic calculus that assigns a geometric interpretation to individual two-qudit gates and tracks their action on stabilizers. For fusion, we prove a general no-go theorem excluding purely unitary protocols for fusing unknown anyon types without introducing ancillas. Remarkably, we show such "input-agnostic" fusion is enabled by simply using a qudit reset. Hence, contrary to folklore, ancilla resources are not needed to braid or fuse non-Abelian anyons (non-Abelions). This work has implications in experimental efforts in error correction: our fusion protocol highlights reset as an underutilized primitive for error correction without the spacetime-overhead of ancillas and measurements.
Related
- Manipulating the stability of crystallographic and magnetic sub-lattices: A first-order magnetoelastic transformation in transition metal based Laves phase
- A New Method For Manipulating Circuits, Application To Quantum Adders
- Probing and Manipulating Quantum Materials with Strong-field Terahertz and Mid-infrared Radiation
- Making Weak Interlayer Excitons Absorb: Manipulating the Effective Oscillator Strength via Purcell Engineering of Critical Coupling
- Computational studies of giant edge islands and unpaired X-points in HSX and W7-X by manipulating coil currents
BibTeX
@misc{lo2026rewire,
title = {{Rewire and reset are all you need: Minimal resources for manipulating non-Abelions}},
author = {Chiu Fan Bowen Lo and Rohith Sajith and Anasuya Lyons and Ashvin Vishwanath and Ruben Verresen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06845},
eprint = {2610.06845},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06845},
}
RIS
TY - UNPB
TI - Rewire and reset are all you need: Minimal resources for manipulating non-Abelions
AU - Chiu Fan Bowen Lo
AU - Rohith Sajith
AU - Anasuya Lyons
AU - Ashvin Vishwanath
AU - Ruben Verresen
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06845
UR - https://arxiv.org/abs/2610.06845
AB - Braiding and fusing anyons are fundamental to topological quantum computation, yet existing circuit protocols often employ ancillas and measurements. We determine the minimal circuit resources for performing such anyon operations in quantum double models of generic finite groups. Our approach braids anyons through a sequential unitary circuit without ancillas. Intuitively, this is obtained by deforming the underlying graph on which the anyons live. More generally, we introduce graph rewiring, a diagrammatic calculus that assigns a geometric interpretation to individual two-qudit gates and tracks their action on stabilizers. For fusion, we prove a general no-go theorem excluding purely unitary protocols for fusing unknown anyon types without introducing ancillas. Remarkably, we show such "input-agnostic" fusion is enabled by simply using a qudit reset. Hence, contrary to folklore, ancilla resources are not needed to braid or fuse non-Abelian anyons (non-Abelions). This work has implications in experimental efforts in error correction: our fusion protocol highlights reset as an underutilized primitive for error correction without the spacetime-overhead of ancillas and measurements.
ER -