Small-world complex network generation on a digital quantum processor

TL;DR

This paper reports the first experimental realization of quantum cellular automata on a digital quantum processor, demonstrating the formation of small-world mutual information networks in a system of up to 23 qubits, with implications for simulating complex quantum systems.

Contribution

It introduces the first experimental implementation of quantum cellular automata on a digital quantum processor, showcasing the generation of small-world networks in a multi-qubit system.

Findings

Successful simulation of QCA on 23 qubits

Formation of small-world mutual information networks

Decoherence occurs at fixed circuit depth regardless of system size

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.