Polyadic braid operators and higher braiding gates
| Autor: | Raimund Vogl, Steven Duplij |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
High Energy Physics - Theory Pure mathematics Algebraic structure Computer Science - Information Theory Braid group General Physics and Astronomy FOS: Physical sciences braid group QC793-793.5 ternary Matrix (mathematics) Quantum gate Computer Science::Emerging Technologies Mathematics::Quantum Algebra Braid qubit Mathematical Physics Physics Quantum Physics Yang–Baxter equation Information Theory (cs.IT) Cartan decomposition Elementary particle physics 16T25 20F36 81P15 81P16 81P40 81P45 81P68 Mathematical Physics (math-ph) braiding quantum gate algebra_number_theory High Energy Physics - Theory (hep-th) Qubit polyadic Quantum Physics (quant-ph) |
| Zdroj: | Universe Volume 7 Issue 8 Universe, Vol 7, Iss 301, p 301 (2021) |
| Popis: | Higher braiding gates, a new kind of quantum gate, are introduced. These are matrix solutions of the polyadic braid equations (which differ from the generalized Yang-Baxter equations). Such gates support a special kind of multi-qubit entanglement which can speed up key distribution and accelerate the execution of algorithms. Ternary braiding gates acting on three qubit states are studied in detail. We also consider exotic non-invertible gates which can be related to qubit loss, and define partial identities (which can be orthogonal), partial unitarity, and partially bounded operators (which can be non-invertible). We define two classes of matrices, the star and circle types, and find that the magic matrices (connected with the Cartan decomposition) belong to the star class. The general algebraic structure of the classes introduced here is described in terms of semigroups, ternary and 5-ary groups and modules. The higher braid group and its representation by higher braid operators are given. Finally, we show that for each multi-qubit state there exist higher braiding gates which are not entangling, and the concrete conditions to be non-entangling are given for the binary and ternary gates discussed. 37 pages, revtex 4.2 |
| Databáze: | OpenAIRE |
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