TY  - JOUR
AU  - Rodriguez-Blanco, Andrea
AU  - Bermudez, Alejandro
AU  - Müller, Markus
AU  - Shahandeh, Farid
TI  - Efficient and Robust Certification of Genuine Multipartite Entanglement in Noisy Quantum Error Correction Circuits
JO  - PRX quantum
VL  - 2
IS  - 2
SN  - 2691-3399
CY  - College Park, MD
PB  - American Physical Society
M1  - FZJ-2021-04547
SP  - 020304
PY  - 2021
AB  - Ensuring the correct functioning of quantum error correction (QEC) circuits is crucial to achieve fault tolerance in realistic quantum processors subjected to noise. The first checkpoint for a fully operational QEC circuit is to create genuine multipartite entanglement (GME) across all subsystems of physical qubits. We introduce a conditional witnessing technique to certify GME that is efficient in the number of subsystems and, importantly, robust against experimental noise and imperfections. Specifically, we prove that the detection of entanglement in a linear number of bipartitions by a number of measurements that also scales linearly, suffices to certify GME. Moreover, our method goes beyond the standard procedure of separating the state from the convex hull of biseparable states, yielding an improved finesse and robustness compared to previous techniques. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version. In particular, we subject the circuits to combinations of three types of noise, namely, uniform depolarizing noise, two-qubit gate depolarizing noise, and bit-flip measurement noise. We numerically compare our method with the standard, yet generally inefficient, fidelity test and to a pair of efficient witnesses, verifying the increased robustness of our method. Last but not least, we provide the full translation of our analysis to a trapped-ion native gate set that makes it suitable for experimental applications.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000674698700001
DO  - DOI:10.1103/PRXQuantum.2.020304
UR  - https://juser.fz-juelich.de/record/902776
ER  -