Quantum logic as superbraids of entangled qubit world lines

TL;DR

This paper introduces a topological framework called superbraids to represent quantum logic, capturing entanglement and quantum crossings of qubit world lines, and linking these to classical link invariants like the Jones polynomial.

Contribution

It develops a novel topological approach to quantum logic using superbraids and introduces quantum skein relations for systematic reduction and analysis.

Findings

Superbraids encode quantum entanglement topologically.

Superlinks can be decomposed into classical links with invariants.

Link invariants are expressed as superpositions of classical invariants.

Abstract

Presented is a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a superbraid. The crossing of world lines is purely quantum in nature, most conveniently expressed analytically with ladder-operator-based quantum gates. At a crossing, independent world lines can become entangled. Complicated superbraids are systematically reduced by recursively applying novel quantum skein relations. If the superbraid is closed (e.g. representing quantum circuits with closed-loop feedback, quantum lattice gas algorithms, loop or vacuum diagrams in quantum field theory), then one can decompose the resulting superlink into an entangled superposition of classical links. In turn, for each member link, one can compute a link invariant, e.g. the Jones polynomial. Thus, a superlink possesses a unique link invariant expressed as an entangled superposition of classical link invariants.