In some aspects, a quantum computing system includes a multi-dimensional array of qubit devices. Coupler devices reside at intervals between neighboring pairs of the qubit devices in the multi-dimensional array. Each coupler device is configured to produce an electromagnetic interaction between one of the neighboring pairs of qubit devices. In some cases, each qubit device has a respective qubit operating frequency that is independent of an offset electromagnetic field experienced by the qubit device, and the coupling strength of the electromagnetic interaction provided by each coupler device varies with an offset electromagnetic field experienced by the coupler device. In some cases, readout devices are each operably coupled to a single, respective qubit device to produce qubit readout signals that indicate the quantum state of the qubit device.