Solutions to higher braid equations
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Abstract
In chapter 10 constant matrix solutions of the polyadic (higher) braid equations are introduced and studied. They play a role as various quantum gates in quantum computation. We define two classes of 8-vertex matrices, star and circle, such that the magic matrices (connected with the Cartan decomposition) belong to the star class. We also define partial identity and unitarity. The general algebraic structure of the classes is described in terms of new semigroups, ternary and 5-ary groups and modules. We present the invertible and noninvertible 8-, 9- and 10-vertex Yang–Baxter maps. We then introduce polyadic braid operators for higher braid equations, find constant matrix solutions for the ternary 8- and 16-vertex cases and give their Pauli matrix presentation.
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| Authors | Steven Duplij |
| Journal | science and technology of advanced materials |
| Year | 2022 |
| DOI |
10.1088/978-0-7503-2648-3ch10
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| URL | |
| Keywords | Keywords not found |
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