Errors in heralded circuits for linear optical entanglement generation

TL;DR

This paper develops a simulation framework using continuous-variable formalism to analyze non-computational leakage errors in heralded photonic entanglement generation, revealing their impact on fault-tolerance.

Contribution

It introduces a novel simulation method for photonic states with leakage errors and evaluates the robustness of Bell state schemes against such errors.

Findings

The five-photon DFT Bell state scheme is most robust to leakage errors.

Leakage errors hinder modular characterization of concatenated gates.

The framework helps identify true noise models for fault-tolerant photonic quantum computing.

Abstract

The heralded generation of entangled states underpins many photonic quantum technologies. As quantum error correction thresholds are determined by underlying physical noise mechanisms, a detailed and faithful characterization of resource states is required. Non-computational leakage, e.g. more than one photon occupying a dual-rail encoded qubit, is an error not captured by standard forms of state tomography, which postselect on photons remaining in the computational subspace. Here we use the continuous-variable (CV) formalism and first quantized state representation to develop a simulation framework that reconstructs photonic quantum states in the presence of partial distinguishability and resulting non-computational leakage errors. Using these tools, we analyze a variety of Bell state generation circuits and find that the five photon discrete Fourier transform (DFT) Bell state generation scheme [Phys Rev. Lett. 126 23054 (2021)] is most robust to such errors for near-ideal photons. Through characterization of a photonic entangling gate, we demonstrate how leakage errors prevent a modular characterization of concatenated gates using current tomographical procedures. Our work is a necessary step in revealing the true noise models that must be addressed in fault-tolerant photonic quantum computing architectures.