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We introduce a simple widely applicable formalism for designing “error-divisible” two-qubit gates: a quantum gate set where fractional rotations have proportionally reduced error compared to the full entangling gate. In current noisy intermediate-scale quantum (NISQ) algorithms, performance is largely constrained by error proliferation at high circuit depths, of which two-qubit gate error is generally the dominant contribution. Further, in many hardware implementations, arbitrary two-qubit rotations must be composed from multiple two-qubit stock gates, further increasing error. This work introduces a set of cri- teria, and example wave forms and protocols to satisfy them, using superconducting qubits with tunable couplers for constructing continuous gate sets with significantly reduced leakage and dynamic ZZ errors for small-angle rotations. If implemented at scale, NISQ-algorithm performance could be significantly improved by our error-divisible gate protocols. 

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.