Factoring isometries of quadratic spaces into reflections
- MathematicsJournal of Algebra
Approximate 3-designs and partial decomposition of the Clifford group representation using transvections
X iv :2 11 1. 13 67 8v 2 [ qu an tph ] 1 9 Ju n 20 22 Approximate 3-designs and partial decomposition of the Clifford group representation using transvections Tanmay Singal∗ Institute of Physics,…
Un-Weyl-ing the Clifford Hierarchy
It can be easily seen that, up to multiplication by a Clifford, every third level unitary is supported on a maximal commutative subgroup of the Pauli group, which implies the generalized semi-Clifford conjecture, proven by Beigi and Shor (2010).
Decomposition of Clifford Gates
- Computer Science2021 IEEE Global Communications Conference (GLOBECOM)
A fast algorithm is provided that decomposes any Clifford gate as a minimal product of Clifford transvections and can be directly used for computing the support of any given Clifford gate.
F eb 2 02 1 Decomposition of Clifford Gates
- Computer Science
A fast algorithm is provided that decomposes any Clifford gate as a minimal product of Clifford transvections and can be directly used for finding all Pauli matrices that commute with any given Clifford gate.
Reflection length in the general linear and affine groups
- MathematicsCommunications in Algebra
Abstract We give an intrinsic criterion to tell whether a reflection factorization in the general linear group is reduced, and give a formula for computing reflection length in the general affine…
Products of reflections in one conjugacy class in the orthogonal group over GF(3)
Let O(V,f) be the orthogonal group, where dim V is finite and f is a nonsingular symmetric bilinear form. Let K = GF(3) be the coordinate field. Let π be an element in the group G which is generated…
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Products of Transvections
- MathematicsCanadian Journal of Mathematics
This paper is concerned with the presentation of certain elements of the group SL(n, K) as products of a minimal number of transvections. To explain the terminology, let V be an n-dimensional left…