Several known algorithms for synthesizing quantum circuits in terms of elementary gates reduce arbitrary computations to diagonal [1, 2]. Circuits for n-qubit diagonal computations can be constructed using one (n − 1)-controlled one-qubit diagonal computation [3] and one inverter per pair of diagonal elements, not unlike the construction of classical AND-OR-NOT circuits based on the lines of a ...

An associahedral set is a combinatorial object generated by Stasheff associahedra {Kn} and equipped with appropriate face and degeneracy operators. Associahedral sets are similar in many ways to simplicial or cubical sets. In this paper we give a formal definition of an associahedral set, discuss some naturally occurring examples and construct an explicit geometric diagonal ∆ : C∗(Kn) −→ C∗(Kn)...

X iv :0 80 6. 12 73 v1 [ m at h. N T ] 7 J un 2 00 8 MATRICIAL FORMULAE FOR PARTITIONS F. AICARDI Abstract. The exponential of the triangular matrix whose entries in the diagonal at distance n from the principal diagonal are all equal to the sum of the inverse of the divisors of n is the triangular matrix whose entries in the diagonal at distance n from the principal diagonal are all equal to t...

Several known algorithms for synthesizing quantum circuits in terms of elementary gates reduce arbitrary computations to diagonal [1, 2]. Circuits for n-qubit diagonal computations can be constructed using one (n − 1)-controlled one-qubit diagonal computation [3] and one inverter per pair of diagonal elements, not unlike the construction of classical AND-OR-NOT circuits based on the lines of a ...

The work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method  and Adomian decomposition method for solving  differential equations of integer and fractional orders.

We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical in...

We study the classical game of peg solitaire when diagonal jumps are allowed. We prove that on many boards, one can begin from a full board with one peg missing, and finish with one peg anywhere on the board. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more jumps by the same peg), and find the shortest solution to the “central game...