Quantum computing with Bianchi groups
| Autor: | Planat, Michel, Aschheim, Raymond, Amaral, Marcelo M., Irwin, Klee |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1051/epjconf/201919800012 |
| Popis: | It has been shown that non-stabilizer eigenstates of permutation gates are appropriate for allowing $d$-dimensional universal quantum computing (uqc) based on minimal informationally complete POVMs. The relevant quantum gates may be built from subgroups of finite index of the modular group $\Gamma=PSL(2,\mathbb{Z})$ [M. Planat, Entropy 20, 16 (2018)] or more generally from subgroups of fundamental groups of $3$-manifolds [M. Planat, R. Aschheim, M.~M. Amaral and K. Irwin, arXiv 1802.04196(quant-ph)]. In this paper, previous work is encompassed by the use of torsion-free subgroups of Bianchi groups for deriving the quantum gate generators of uqc. A special role is played by a chain of Bianchi congruence $n$-cusped links starting with Thurston's link. Comment: 10 pages, 14 figures, 3 tables a mistake occured in the fourth author name. arXiv admin note: text overlap with arXiv:1802.04196 |
| Databáze: | arXiv |
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