Atom-Mediated Deterministic Generation and Stitching of Photonic Graph States

Highly entangled multiphoton graph states are a crucial resource in photonic quantum computation and communication. Yet, the lack of photon-photon interactions makes the construction of such graph states especially challenging. Typically, these states are produced through probabilistic single-photon sources and linear-optics entangling operations that require indistinguishable photons. The resulting inefficiency of these methods necessitates a large overhead in the number of sources and operations, creating a major bottleneck in the photonic approach. Here, we show how harnessing single-atom-based photonic operations can enable deterministic generation of photonic graph states, while also lifting the requirement for photon indistinguishability. To this end, we introduce a multigate quantum node comprising a single atom in a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>W</a:mi></a:math>-type level scheme coupled to an optical resonator. This configuration provides a versatile toolbox for generating graph states, allowing the operation of both the controlled-<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:mi>Z</d:mi></d:math> and photon-atom gates, as well as the deterministic generation of single photons. Furthermore, the ability to deterministically entangle photonic qubits enables the expansion of the generated state by stitching together graph states produced by different nodes. We investigate the implementation of this gate-based approach using <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><g:msup><g:mi/><g:mn>87</g:mn></g:msup><g:mi>Rb</g:mi></g:math> atoms and evaluate its performance through numerical simulations.