In an illustrative run of a distance-5 bit-flip repetition code (5 data qubits)
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Quantum Information & Technology · Open quantum systems, decoherence and error correction
Quantum Information and Technology, Ch Quantum error correction
Problem
In an illustrative run of a distance-5 bit-flip repetition code (5 data qubits), styled after the repetition-code demonstrations of Chen et al., Nature 595, 383 (2021), on a superconducting processor: the code is run for 20000 error-correction rounds of equal duration, and 51 logical bit-flip events are observed in total. On the same processor, the best single physical qubit, left idle for the duration of one round with every other qubit also operating, flips with probability 8.0×10−4 per round.
((a)) Estimate the logical error probability per round, pL, together with its binomial standard error.
((b)) Decide, with a reason, whether this logical qubit has reached break-even against the best physical qubit on this processor.