Small-world complex network generation on a digital quantum processor
Abstract
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. For instance, Goldilocks QCA depending on trade-off principles exhibit non-equilibrating coherent dynamics and generate complex mutual information networks, much like the brain. The inability of classical computers to simulate large quantum systems is a hindrance to understanding the physics of quantum cellular automata, but quantum computers offer an ideal simulation platform. Here we demonstrate the first experimental realization of QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. Employing low-overhead calibration and error mitigation techniques, we calculate population dynamics and complex network measures indicating the formation of small-world mutual information networks. Unlike random states, these networks decohere at fixed circuit depth independent of system size; the largest of which corresponds to 1,056 two-qubit gates. Such computations may open the door to the employment of QCA in applications like the simulation of strongly-correlated matter or beyond-classical computational demonstrations.
Cite
@article{arxiv.2111.00167,
title = {Small-world complex network generation on a digital quantum processor},
author = {Eric B. Jones and Logan E. Hillberry and Matthew T. Jones and Mina Fasihi and Pedram Roushan and Zhang Jiang and Alan Ho and Charles Neill and Eric Ostby and Peter Graf and Eliot Kapit and Lincoln D. Carr},
journal= {arXiv preprint arXiv:2111.00167},
year = {2022}
}