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We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deter-ministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state. A cellular automaton (CA) is a discrete dynamical system… (More)
We propose a box and ball system with a periodic boundary condition (pBBS). The time evolution rule of the pBBS is represented as a Boolean recurrence formula, an inverse ultradiscretization of which is shown to be equivalent with the algorithm of the calculus for the 2N th root. The relations to the pBBS of the combinatorial R matrix of U ′ q (A (1) N) are… (More)
Since Grover Demonstrated the database search algorithm , many applications of this algorithm have been studied [1, 2]. The quantum counting  is one of the most important applications with using the quantum Fourier transform. Given a quantum oracle, the quantum counting can find the number t of solutions of the oracle through in unordered N elements… (More)
We show that the entanglement cost of the three-dimensional antisym-metric states is one ebit. The concept of entanglement is the key for quantum information processing. To quantify the resource of entanglement, its measures should be additive, such as bits for classical information. One candidate for such additive measures is entanglement of formation. In… (More)
We show that the Hankel determinants of a generalized Catalan sequence satisfy the equations of the elliptic sequence. As a consequence, the coordinates of the multiples of an arbitrary point on the elliptic curve are expressed by the Hankel determinants.