The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C0,2. This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enab...

A Moyal deformation of a Clifford Cl(3, 1) Gauge Theory of (Conformal) Gravity is performed for canonical noncommutativity (constant Θ parameters). In the very special case when one imposes certain constraints on the fields, there are no first order contributions in the Θ parameters to the Moyal deformations of Clifford gauge theories of gravity. However, when one does not impose constraints on...

We demonstrate the emergence of the conformal group SO(4,2) from the Clifford algebra of spacetime. The latter algebra is a manifold, called Clifford space, which is assumed to be the arena in which physics takes place. A Clifford space does not contain only points (events), but also lines, surfaces, volumes, etc..., and thus provides a framework for description of extended objects. A subspace ...

we present the basic results on the representation theory of the alternating groups. our approach is based on clifford theory.

In our combinatorial universe, matter grows in a particular way, according to specific steps. The (n + 1) character of this growth lends itself easily to the Clifford Algebra and Clifford Spinor spaces which develop in the fashion of Mount Meru or Pascal’s Triangle. This style of development leads to Fibonacci Numbers and the Golden Section which implies that these concepts are deeply entwined ...

Peres/Mermin arguments about no-hidden variables in quantummechanics are used for displaying a pair (R,S) of entangling Clifford quantum gates, acting on two qubits. From them, a natural unitary realization of Coxeter/Weyl groups W (D5) and W (F4) emerges, which is also reflected into the splitting of the n-qubit Clifford group Cn into group dipoles C± n . The union of the three-qubit real Clif...

— In this paper we show that the invariant polynomial ring of the associated Clifford-Weil group can be embedded into the ring of Jacobi modular forms over the totally real field, so, therefore, that of Hilbert modular forms over the totally real field. Résumé (Anneau des invariants du groupe de Clifford-Weil, et forme de Jacobi sur un corps totallement réel) Dans cet article nous démontrons qu...

The Gottesman-Knill theorem states that every “Clifford” quantum circuit, i.e., a circuit composed of Hadamard, CNOT and phase gates, can be simulated efficiently on a classical computer. It is was later found that a highly restricted classical computer (using only NOT and CNOT gates) suffices to simulate all Clifford circuits, implying that these circuits are most likely even significantly wea...

Magic state distillation is a fundamental technique for realizing fault-tolerant universal quantum computing, and produces high-fidelity Clifford eigenstates, called magic states, which can be used to implement the non-Clifford π/8 gate. We propose an efficient protocol for distilling other non-stabilizer states that requires only Clifford operations, measurement, and magic states. One critical...