Local invariants of braiding quantum gates -- associated link polynomials and entangling power

Abstract

For a generic $n$-qubit system, local invariants under the action of $SL(2,\mathbb{C}{)}^{\otimes n}$ characterize non-local properties of entanglement. In general, such properties are not immediately apparent and hard to construct. Here we consider certain two-qubit Yang-Baxter operators, which we dub of the `X-type', and show that their eigenvalues completely determine the non-local properties of the system. Moreover, we apply the Turaev procedure to these operators and obtain their associated link/knot polynomials. We also compute their entangling power and compare it with that of a generic two-qubit operator.

arXiv comment43 pages, Published version

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Cited by in corpus (6)

• Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras
• Optimal realization of Yang-Baxter gate on quantum computers
• Algebraic classification of Hietarinta's solutions of Yang-Baxter equations~:~invertible $4\times 4$ operators
• Polyadic braid operators and higher braiding gates
• Geometric representations of braid and Yang-Baxter gates
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations