Entangling gates from cabling of knots

TL;DR

This paper proposes a novel method for constructing high-fidelity two-qubit entangling gates in topological quantum computers using knot theory cabling, enabling more reliable quantum operations.

Contribution

It introduces a new approach to realize two-qubit gates via knot cabling, improving operational fidelity and entanglement in topological quantum computing.

Findings

Cabling-based braiding can produce entangling two-qubit gates.

The method maintains high fidelity with low probability of leaving computational space.

Examples demonstrate the effectiveness of the approach for various parameters.

Abstract

While there is a general consensus about the structure of one qubit operations in topological quantum computer, two qubits are as usual a more difficult and complex story of different attempts with varying approaches, problems and effectiveness. In this paper we discuss how to construct an efficient realization of a two qubit gate in topological quantum computer, by using principle of cabling from the knot theory. This allows to construct a braiding of cables dependent on the parameters of the theory where there is a low probability of moving out of computational space (high fidelity of operation) while there is a non-trivial entangling two-qubit operation. We also present some examples of these operations for different parameters of the theory.