Probabilistic cellular automata (CA) provides a classic framework for studying non-equilibrium statistical physics on lattices. A notable example is the Domany-Kinzel CA, which has been used to investigate process of directed percolation and critical dynamics phase transition betweeen absorbing percolating phases. In this work, we construct non-unitary Quantum Cellular Automaton that generalise...

We construct a three-dimensional quantum cellular automaton (QCA), an automorphism of the local operator algebra on lattice qubits, which disentangles ground state Walker–Wang three-fermion model. show that if this QCA can be realized by circuit constant depth, then there exists two-dimensional commuting projector Hamiltonian realizes topological order is widely believed not to possible. conjec...

We formulate a new paradigm for computing with cellular automata (CAS) composed of arrays of quantum devices-quantum cellular automata. Computing in such a paradigm is edge driven. Input, output, and power are delivered at the edge of the cnarray only; no direct flow of information or energy to internal cells is required. Computing in this paradigm is also computing with the ground state. The a...