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 () and Lincoln D. Carr ()
Additional contact information
Eric B. Jones: National Renewable Energy Laboratory
Logan E. Hillberry: University of Texas
Matthew T. Jones: Colorado School of Mines
Mina Fasihi: Colorado School of Mines
Pedram Roushan: Google Quantum AI
Zhang Jiang: Google Quantum AI
Alan Ho: Google Quantum AI
Charles Neill: Google Quantum AI
Eric Ostby: Google Quantum AI
Peter Graf: National Renewable Energy Laboratory
Eliot Kapit: Colorado School of Mines
Lincoln D. Carr: Colorado School of Mines

Nature Communications, 2022, vol. 13, issue 1, 1-7

Abstract: 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. The inability of classical computers to simulate large quantum systems hinders the elucidation of quantum cellular automata, but quantum computers offer an ideal simulation platform. Here, we experimentally realize QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. We calculate calibrated and error-mitigated population dynamics and complex network measures, which indicate the formation of small-world mutual information networks. These networks decohere at fixed circuit depth independent of system size, the largest of which corresponding to 1,056 two-qubit gates. Such computations may enable the employment of QCA in applications like the simulation of strongly-correlated matter or beyond-classical computational demonstrations.

Date: 2022
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DOI: 10.1038/s41467-022-32056-y

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