  Multi-qubit parity measurements are at the core of many quantum error
correction schemes. Extracting multi-qubit parity information typically
involves using a sequence of multiple two-qubit gates. In this paper, we
propose a superconducting circuit device with native support for multi-qubit
parity-controlled gates (PCG). These are gates that perform rotations on a
parity ancilla based on the multi-qubit parity operator of adjacent qubits, and
can be directly used to perform multi-qubit parity measurements. The circuit
consists of a set of concatenated Josephson ring modulators and effectively
realizes a set of transmon-like qubits with strong longitudinal
nearest-neighbor couplings. PCGs are implemented by applying microwave drives
to the parity ancilla at specific frequencies. We investigate the scheme's
performance with numerical simulation using realistic parameter choices and
decoherence rates, and find that the device can perform four-qubit PCGs in 30
ns with process fidelity surpassing 99%. Furthermore, we study the effects of
parameter disorder and spurious coupling between next-nearest neighboring
qubits. Our results indicate that this approach to realizing PCGs constitute an
interesting candidate for near-term quantum error correction experiments.
