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The heralded generation of entangled states underpins many photonic quantumtechnologies. As quantum error correction thresholds are determined byunderlying physical noise mechanisms, a detailed and faithful characterizationof resource states is required. Non-computational leakage, e.g. more than onephoton occupying a dual-rail encoded qubit, is an error not captured bystandard forms of state tomography, which postselect on photons remaining inthe computational subspace. Here we use the continuous-variable (CV) formalismand first quantized state representation to develop a simulation framework thatreconstructs photonic quantum states in the presence of partialdistinguishability and resulting non-computational leakage errors. Using thesetools, we analyze a variety of Bell state generation circuits and find that thefive photon discrete Fourier transform (DFT) Bell state generation scheme [PhysRev. Lett. 126 23054 (2021)] is most robust to such errors for near-idealphotons. Through characterization of a photonic entangling gate, we demonstratehow leakage errors prevent a modular characterization of concatenated gatesusing current tomographical procedures. Our work is a necessary step inrevealing the true noise models that must be addressed in fault-tolerantphotonic quantum computing architectures.

Errors in heralded circuits for linear optical entanglement generation