Artificial atoms nonlocally coupled to waveguides—the so-called giant atoms—offer opportunities for the control of light and matter. In this work, we show how to use an array of nonlocally coupled transmon “molecules” to engineer a passive photonic controlled gate for waveguide photons. In particular, we show that a conditional elastic phase shift between counterpropagating photons arises from the interplay between direction-dependent couplings, engineered through an interplay of nonlocal interactions and molecular binding strength; and the nonlinearity of the transmon array. We analyze the conditions under which a maximal $\pi$-phase shift—and hence a CZ gate—is obtained, and characterize the gate fidelity as a function of key experimental parameters, including finite transmon nonlinearities, emitter spectral inhomogeneities, and limited cooperativity. Our work opens the use of giant atoms as key elements of microwave photonic quantum computing devices.

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• Circuit quantum electrodynamics
• Photonics
• Quantum information with atoms & light
• Quantum information with solid state qubits
• Quantum optics with artificial atoms
• Superconducting quantum optics
• Superconducting qubits
• Waveguides