On generalized Clifford algebraC 4 (n) andGL q (2;C) quantum group

On Generalized Clifford Algebra C (n) 4 and GLq(2; C) Quantum Group A.K.Kwa´sniewski

The Hidden Quantum Group of the 8–vertex Free Fermion Model: q–Clifford Algebras

We prove in this paper that the elliptic R–matrix of the eight vertex free fermion model is the intertwiner R–matrix of a quantum deformed Clifford–Hopf algebra. This algebra is constructed by affinization of a quantum Hopf deformation of the Clifford algebra. IMAFF-2/93 February 1993

Semi-Clifford and Generalized Semi-Clifford Operations

Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory. Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and Clifford operators can be applied fault-tolerantly. Indeed, this technique can be generalized for an extended set of gates, the so called Ck hierarchy gates, intro...

Generalized clifford groups and simulation of associated quantum circuits

Quantum computations that involve only Clifford operations are classically simulable despite the fact that they generate highly entangled states; this is the content of the Gottesman-Knill theorem. Here we isolate the ingredients of the theorem and provide generalisations of some of them with the aim of identifying new classes of simulable quantum computations. In the usual construction, Cliffo...

Representations and Q-Boson Realization of The Algebra of Functions on The Quantum Group GLq(n)

We present a detailed study of the representations of the algebra of functions on the quantum group GLq(n). A q-analouge of the root system is constructed for this algebra which is then used to determine explicit matrix representations of the generators of this algebra. At the end a q-boson realization of the generators of GLq(n) is given.