Solvable states for ternary-unitary gates

Recently we introduced the so-called ternary unitary quantum gates. These are four-particle gates acting in 2+1-dimensions and are unitary in time and both spatial dimensions. Now we generalise the concept of solvable matrix product state(Phys. Rev. B 101, 094304) to two spatial dimensions under cylindrical boundary conditions. We show that such solvable PEPS can be identified with matrix product unitaries. In the resulting tensor network for evaluating equal-time correlation functions, the bulk ternary unitary gates cancel out, and we delineate and implement a numerical algorithm for computing such correlations.     «

Recently we introduced the so-called ternary unitary quantum gates. These are four-particle gates acting in 2+1-dimensions and are unitary in time and both spatial dimensions. Now we generalise the concept of solvable matrix product state(Phys. Rev. B 101, 094304) to two spatial dimensions under cylindrical boundary conditions. We show that such solvable PEPS can be identified with matrix product unitaries. In the resulting tensor network for evaluating equal-time correlation functions, the bul...     »