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...

Abstract A classical theorem of Balcar, Pelant, and Simon says that there is a base matrix height ${\mathfrak h}$ , where the distributivity number ${\cal P} (\omega ) / {\mathrm {fin}}$ . We show if continuum c}$ regular, then are matrices any regular uncountable $\leq {\mathfrak in Cohen random models. This answers questions Fischer, Koelbing, Wohofsky.

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 ...

Spatial reasoning is one of the central tasks in Computer Vision. It always has to deal with uncertain data. Projective geometry has become the working horse for modelling multiple view geometry, while modelling uncertainty with statistical tools has become a standard. Geometric reasoning in projective geometry with uncertain geometric elements has been advocated by Kanatani in the early 90’s, ...

Recently Daviau showed the equivalence of ordinary matrix based Dirac theory –formulated within a spinor bundle Sx ≃ C 4 x–, to a Clifford algebraic formulation within space Clifford algebra Cl(R, δ) ≃ M2(C) ≃ P ≃ Pauli algebra (matrices) ≃ H ⊕ H ≃ biquaternions. We will show, that Daviau’s map θ : C 7→ M2(C) is an isomorphism. Furthermore it is shown that Hestenes’ and Parra’s formulations are...