Clifford algebras, Spin groups and qubit trees
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Representations of Spin groups and Clifford algebras derived from structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deleting of superfluous branches. Usual Jordan-Wigner construction also may be formally obtained in such approach by bringing the process up to trivial qubit chain ("trunk"). The methods can be also used for effective simulations of some quantum circuits corresponding to the binary tree structure. Modeling of more general qubit trees and relation with mapping used in Bravyi-Kitaev transformation are also briefly outlined.
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