Quantum logic as superbraids of entangled qubit world lines

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.