相关论文: Clifford's theorem for coherent systems
The term Clifford group was introduced in 1998 by D. Gottesmann in his investigation of quantum error-correcting codes. The simplest Clifford group in multiqubit quantum computation is generated by a restricted set of unitary Clifford gates…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
An algebraic description of basic discrete symmetries (space inversion P, time reversal T, charge conjugation C and their combinations PT, CP, CT, CPT) is studied. Discrete subgroups {1,P,T,PT} of orthogonal groups of multidimensional…
The Clifford spectrum is an elegant way to define the joint spectrum of several Hermitian operators. While it has been know that for examples as small as three $2$-by-$2$ matrices the Clifford spectrum can be a two-dimensional manifold, few…
In this paper, theory and construction of spinor representations of real Clifford algebras $\cl_{p,q}$ in minimal left ideals are reviewed. Connection with a general theory of semisimple rings is shown. The actual computations can be found…
In this paper we present a generalization of the Fueter's theorem for monogenic functions to the case of the biregular functions of Clifford analysis.
Quantum multiparameter deformation of real Clifford algebras is proposed. The corresponding irreducible representations are found.
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
We use Clifford algebras to construct a unified formalism for studying constant extrinsic curvature immersed surfaces in riemannian and semi-riemannian $3$-manifolds in terms of immersed bilegendrian surfaces in their unitary bundles. As an…
Using a Cayley complex (generalizing the Cayley graph) and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index 1.
The purpose of this shord paper is to make the link between the fundamental work of Atiyah, Bott and Shapiro (MR0167985/29/5250) and twisted K-theory (MR0282363/43/8075). This link was implicit for a long time in the literature (for the…
In the present work we are concerned with the development of a new uncertainty principle based on wavelet transform in the Clifford analysis/algebras framework. We precisely derive a sharp Heisenberg-type uncertainty principle for the…
Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…
We prove a fractional Noether's theorem for fractional Lagrangian systems invariant under a symmetry group both in the continuous and discrete cases. This provides an explicit conservation law (first integral) given by a closed formula…
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
Clifford gates and transformations, which map products of elementary Pauli or Majorana operators to other such products, are foundational in quantum computing, underpinning the stabilizer formalism, error-correcting codes, magic state…
Recently, a new embedding/compactness theorem for integral currents in a sequence of metric spaces has been established by the second author. We present a version of this result for locally integral currents in a sequence of pointed metric…
The n-qubit Pauli group and its normalizer the n-qubit Clifford group have applications in quantum error correction and device characterization. Recent applications have made use of the representation theory of the Clifford group. We apply…
This paper studies robustness of multivariable systems with parametric uncertainties, and establishes a multivariable version of Edge Theorem. An illustrative example is presented.
Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit real…