An optimization framework for deterministic generation of photonic graph states

Photonic graph states are key resources in quantum computing and communications, but are challenging to realize due to the difficulty of photon-photon interactions. Deterministic methods of multi-photon entanglement creation leverage quantum emitter qubits, e.g., quantum dots, to establish and transfer entanglement to photons, and can minimize the resource overheads seen in probabilistic methods. However, there are still limitations in which quantum circuits, i.e., the necessary sequence of quantum gates required to create a target state, can be experimentally implemented due to constraints such as emitter coherence times and CNOT connectivity. While devising optimized state-generating circuits is crucial to experimentally realize photonic graph states, it is a highly non-trivial task. We introduce an optimization method for deterministic generation of photonic graph states considering cost metrics such as circuit depth and gate count which is based on the local Clifford (LC) equivalency of quantum states. Applied to the special case of repeater graph states, we achieve a reduction of up to 50% in the number of CNOT gates. The LC-enhanced circuit design brings us closer to the experimental realization of generation protocols for large photonic graph states, which are crucial for loss and error tolerant quantum protocols, and long range quantum communications.