Generalized Clifford-Littlewood-Eckmann groups
نویسندگان
چکیده
منابع مشابه
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...
متن کاملSemi-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...
متن کاملClifford Periodicity from Finite Groups
We deduce the periodicity 8 for the type of Pin and Spin representations of the orthogonal groups O(n) from simple combinatorial properties of the finite Clifford groups generated by the gamma matrices. We also include the case of arbitrary signature O(p, q). The changes in the type of representation can be seen as a rotation in the complex plane. The essential result is that adding a (+) dimen...
متن کاملClifford Algebras and Spin Groups
We’ll now turn from the general theory to examine a specific class class of groups: the orthogonal groups. Recall that O(n,R) is the group of n by n orthogonal matrices (the group preserving the standard inner product on R). This group has two components, with the component of the identity SO(n,R), the orthogonal matrices of determinant 1. We’ll mostly restrict attention to SO(n,R). An importan...
متن کاملOn Averaging in Clifford Groups
Averaging measured data is an important issue in computer vision and robotics. Integrating the pose of an object measured with multiple cameras into a single mean pose is one such example. In many applications data does not belong to a vector space. Instead, data often belongs to a non–linear group manifold as it is the case for orientation data and the group of three–dimensional rotations SO(3...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1991
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1991.149.157