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arXiv · 2111.00167

Small-world complex network generation on a digital quantum processor

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
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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.

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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. 2021-10-30. Small-world complex network generation on a digital quantum processor. https://doi.org/10.1038/s41467-022-32056-y

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