Entangling gates from cabling of knots

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.

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Comparing Quantum Entanglement and Topological Entanglement
• Colored HOMFLY polynomials of knots presented as double fat diagrams
• Colored HOMFLY polynomials for the pretzel knots and links
• Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
• Probing Majorana localization in minimal Kitaev chains through a quantum dot
• Multiplicity-free quantum 6j-symbols for U_q(sl_N)
• Tabulating knot polynomials for arborescent knots
• Towards topological quantum computer
• Multiplicity-free $U_q(s{l}_N)$ 6-j symbols: relations, asymptotics, symmetries
• Quantum $\mathcal{R}$-matrices as universal qubit gates
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• On measuring the topological charge of anyons
• Entangled states from arborescent knots

Cited by in corpus (1)

• The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm