Efficient and Robust Certification of Genuine Multipartite Entanglement in Noisy Quantum Error Correction Circuits

Ensuring the correct functioning of quantum error correction (QEC) circuits is crucial to achieve fault tolerance in realistic processors subjected noise. The first checkpoint for a fully operational QEC circuit create genuine multipartite entanglement (GME) across all subsystems physical qubits. We introduce conditional witnessing technique certify GME that efficient number and, importantly, robust against experimental noise and imperfections. Specifically, we prove detection linear bipartitions by measurements also scales linearly, suffices GME. Moreover, our method goes beyond standard procedure separating state from convex hull biseparable states, yielding an improved finesse robustness compared previous techniques. apply noisy readout stabilizer operators distance-three topological color code its flag-based fault-tolerant version. In particular, subject combinations three types noise, namely, uniform depolarizing two-qubit gate bit-flip measurement numerically compare with standard, yet generally inefficient, fidelity test pair witnesses, verifying increased method. Last but not least, provide full translation analysis trapped-ion native set makes it suitable applications.12 MoreReceived 3 November 2020Accepted 5 March 2021DOI:https://doi.org/10.1103/PRXQuantum.2.020304Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasQuantum entanglementQuantum correctionQuantum information processingQuantum Information