aiqbench analysis
This research proposes a novel paradigm for neuromorphic computation by replacing traditional gradient descent with combinatorial optimization over braid groups derived from topological exceptional points. By encoding learning tasks into discrete braiding operations, the framework aims to achieve inherent noise immunity and prevent catastrophic forgetting through mathematical construction rather than empirical tuning. This work represents a significant theoretical advance in leveraging non-Hermitian physics for robust quantum machine learning architectures.
Topologically Protected Learning from Exceptional Point Braiding: Toward Braid Programming
arXiv:2608.15829v1 Announce Type: new Abstract: We present a framework for topological learning based on exceptional point (EP) braiding in a non-Hermitian Bogoliubov-de Gennes Hamiltonian. A closed algebraic equation for the EP super-surface is derived; through momentum quantisation in finite systems, it predicts the exact number and parameter positions of all EPs in real space, irrespective of system size. The EP topology is characterised by two quantised invariants the state-swap fidelity and the normalised Berry phase which cannot both be zero for a topological EP. A complete topological map shows that all EPs lie within a specefic region. Adiabatic encirclements confirm robust state swapping and yield a universal set of braid gates, including Pauli-X, Pauli-Y, Pauli-Z, a Hadamard-like gate, the T-gate, and a SWAP operation, with the special case where a is 0, providing additional phase gates. Building on these generators, we reformulate learning as braid programming a discrete search over the braid group that replaces gradient descent on continuous weights with combinatorial optimisation. A proof-of-concept genetic search successfully discovers short braid words that reproduce the standard Hadamard gate and the H.Z gate with perfect fidelity. This paradigm offers inherent noise immunity, catastrophic-forgetting prevention through compositional concatenation, and guaranteed generalisation by mathematical construction, establishing EP braiding as a promising substrate for robust, interpretable, and topologically protected neuromorphic computation.
Abstract:We present a framework for topological learning based on exceptional point (EP) braiding in a non-Hermitian Bogoliubov-de Gennes Hamiltonian. A closed algebraic equation for the EP super-surface is derived; through momentum quantisation in finite systems, it predicts the exact number and parameter positions of all EPs in real space, irrespective of system size. The EP topology is characterised by two quantised invariants the state-swap fidelity and the normalised Berry phase which cannot both be zero for a topological EP. A complete topological map shows that all EPs lie within a specefic region. Adiabatic encirclements confirm robust state swapping and yield a universal set of braid gates, including Pauli-X, Pauli-Y, Pauli-Z, a Hadamard-like gate, the T-gate, and a SWAP operation, with the special case where a is 0, providing additional phase gates. Building on these generators, we reformulate learning as braid programming a discrete search over the braid group that replaces gradient descent on continuous weights with combinatorial optimisation. A proof-of-concept genetic search successfully discovers short braid words that reproduce the standard Hadamard gate and the H.Z gate with perfect fidelity. This paradigm offers inherent noise immunity, catastrophic-forgetting prevention through compositional concatenation, and guaranteed generalisation by mathematical construction, establishing EP braiding as a promising substrate for robust, interpretable, and topologically protected neuromorphic computation.
Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)
arXiv:2608.15829 [quant-ph]
(or arXiv:2608.15829v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.15829 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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