Small-world complex network generation on a digital quantum processor

Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. This paper experimentally realizes QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. The formation of small-world mutual information networks is observed, which decohere at a fixed circuit depth independent of system size. These computations suggest potential applications of QCA in simulating strongly-correlated matter or beyond-classical computational demonstrations.

Eric B. Jones, Logan E. Hillberry, Matthew T. Jones, Mina Fasihi, Pedram Roushan, Zhang Jiang, Alan Ho, Charles Neill, Eric Ostby, Peter Graf, Eliot Kapit, Lincoln D. Carr