UNITARITY IN ONE DIMENSIONAL NONLINEAR QUANTUM CELLULAR AUTOMATA

摘要: Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, particular, are tightly constrained. In previous work we proved a simple No-go Theorem which precludes nontrivial homogeneous for linear quantum automata. Here carefully define general automata order to investigate possibility that there be unitary when local rule nonlinear. Since transition amplitudes constructed from product amplitudes, infinite lattices require different treatment than periodic ones. We prove Theorems both cases, expressing equivalence 1+1 dimensions unitarity and certain sets constraints rule, then show these can solved give variety multiparameter families nonlinear The Theorems, together with Surjectivity case, also imply decidable one dimensional