Synthetic frequency dimensions offer a powerful approach in the simulation of lattice models and control photon dynamics. However, extending this concept to the quantum regime, particularly at the single-photon level, has remained challenging in photonic platforms. Here, we demonstrate quantum-state initialization and detection of single-photon evolutions within a synthetic frequency lattice by integrating a superconducting qubit with a 16 m aluminum coaxial cable. A tunable superconducting quantum interference device–based modulator is employed to synthesize lattice couplings and artificial gauge fields. We observe single-photon quantum random walks and Bloch oscillations, as well as nonadiabatic unidirectional frequency conversion under rapid temporal modulation of the lattice Hamiltonian, and present band-structure measurements. The lattice connectivity can be readily reconfigured to construct higher-dimensional lattices using a multiplicity of drive tones. Our results establish superconducting quantum circuits as a versatile platform for programmable Hamiltonians and extensible synthetic lattices with flexible single-photon control.

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• Optical quantum information processing
• Photonics
• Quantum information with solid state qubits
• Quantum simulation
• Superconducting quantum optics
• Synthetic gauge fields
• Superconducting qubits
• Microwave techniques