CO$Φ$ - COmpiling PHotonics into dIgital quantum circuits

Photonic and qubit-based (digital) approaches to quantum computing are largely regarded as separate paradigms. This article aims to bridge these paradigms by developing a method for mapping quantum-optical systems onto qubit-based quantum circuits. The key ingredient enabling this mapping is the introduction of a truncation of the Fock space describing single-mode optical states. Within this framework, representations of basic photonic operations are developed, including the phase-rotation operator, the displacement operator, the squeezing operator, and the beam splitter. Explicit quantum circuit constructions are provided for Fock-space truncations of dimension $N=2$ and $N=4$. We discuss benchmarking of the implemented operations and identify the regime of applicability and the limitations of the proposed method. The presented results can be used to simulate quantum optical circuits on qubit-based quantum computers, with special relevance to Gaussian Boson Sampling in the low-photon-number regime. To demonstrate the practical applicability of this approach, we complement the theoretical framework with a Python-based quantum programming tool CO$Φ$ that compiles Blackbird quantum-optics programs into qubit-based OpenQASM circuits using a truncated Fock-space encoding. The compiler is available on GitHub at https://github.com/Quantum-Cosmos-Lab/cophi.