Complexified spacetime algebra is defined as the geometric (Clifford) algebra of spacetime with complex coefficients. By resorting to matrix representation by means of Dirac-Pauli gamma matrices, the paper demonstrates isomorphism between subalgebras of CSTA and SU(3). It is shown that the symmetry group of those subalgebras is indeed U(1) ⊗ SU(2) ⊗ SU(3) and that there are 4 distinct copies of...

Given a real representation of the Clifford algebra corresponding to Rp+q with metric of signature (p, q), we demonstrate the existence of two natural bilinear forms on the space of spinors. With the Clifford action of k-forms on spinors, the bilinear forms allow us to relate two spinors with elements of the exterior algebra. From manipulations of a rank four spinorial tensor introduced in [1],...

The orthogonal simple group 0 (3) has three conjugacy classes of maximal subgroups the form 36:L4(3). These groups are all isomorphic to each other and order 4421589120 with index 1120 in (3). In this paper, we will compute ordinary carácter table one these using technique Fischer-Clifford matrices. This is very efficient character an extension Ḡ = N.G especially where normal subgroup N element...

We describe a new method for the decomposition of an arbitrary n qubit operator with entries in Z[i, 1 √ 2 ], i.e., of the form a+b √ 2+i(c+d √ 2) √ 2 k , into Clifford+T operators where n ≤ 2. This method achieves a bound of O(k) gates using at most one ancilla using decomposition into 1and 2-level matrices which was first proposed by Giles and Selinger in [2].

We propose a family of error-detecting stabilizer codes with an encoding rate of 1/3 that permit a transversal implementation of the gate T = exp (−iπZ/8) on all logical qubits. These codes are used to construct protocols for distilling high-quality “magic” states T |+〉 by Clifford group gates and Pauli measurements. The distillation overhead scales asO( log (1/ )), where is the output accuracy...

The String Uncertainty Relations have been known for some time as the stringy corrections to the original Heisenberg's Uncertainty principle. In this letter the Stringy Uncertainty relations, and corrections thereof, are explicitly derived from the New Relativity Principle that treats all dimensions and signatures on the same footing and which is based on the postulate that the Planck scale is ...