Experimental realization of a bidirectional quantum analog-to-digital converter between photonic wavefront and qubits.

Quantum systems can be fundamentally classified into discrete-variable (DV) and continuous-variable (CV) systems. The degree of quantum advantage achieved with a quantum system is often dictated by the scalability, robustness, and operational feasibility-factors that are closely tied to the nature of the variables employed. Notably, DV and CV systems are largely complementary in these factors. Consequently, integrating DV and CV variables holds significant promise for overcoming the inherent challenges associated with relying solely on one type of variable system. In this study, we build a bidirectional quantum analog-to-digital converter (QADC/QDAC), which facilitates deterministic and reversible quantum information transfer between CV and DV systems. This QADC/QDAC is hardware-efficient, and the error decreases exponentially with the number of qubits, thereby allowing high-fidelity information transfer with a few qubits. With this photonic QADC/QDAC, we demonstrate efficient CV mode tomography leveraging DV tomography techniques and achieve deterministic generation of non-Gaussian CV mode from qubits. Our findings address a critical barrier in constructing hybrid quantum processors and open up new avenues for scientific exploration previously inaccessible to single-variable quantum systems.