Fredkin Spin Chain

  title={Fredkin Spin Chain},
  author={Olof Salberger and Vladimir E. Korepin},
  journal={arXiv: Quantum Physics},
We introduce a new model of interacting spin 1/2. It describes interaction of three nearest neighbors. The Hamiltonian can be expressed in terms of Fredkin gates. The Fredkin gate (also known as the CSWAP gate) is a computational circuit suitable for reversible computing. Our construction generalizes the work of Ramis Movassagh and Peter Shor. Our model can be solved by means of Catalan combinatorics in the form of random walks on the upper half of a square lattice [Dyck walks]. Each Dyck path… 

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