Performance of surface codes in realistic quantum hardware
Surface codes are generally studied based on the assumption that each of the
qubits that make up the surface code lattice suffers noise that is independent
and identically distributed (i.i.d.). However, real benchmarks of the
individual relaxation ($T_1$) and dephasing ($T_2$) times of the constituent
qubits of state-of-the-art quantum processors have recently shown that the
decoherence effects suffered by each particular qubit actually vary in
intensity. In consequence, in this article we introduce the independent
non-identically distributed (i.ni.d.) noise model, a decoherence model that
accounts for the non-uniform behaviour of the docoherence parameters of qubits.
Additionally, we use the i.ni.d model to study how it affects the performance
of a specific family of Quantum Error Correction (QEC) codes known as planar
codes. For this purpose we employ data from four state-of-the-art
superconducting processors: ibmq\_brooklyn, ibm\_washington, Zuchongzhi and
Rigetti Aspen-M-1. Our results show that the i.i.d. noise assumption
overestimates the performance of surface codes, which can suffer up to $95\%$
performance decrements in terms of the code pseudo-threshold when they are
subjected to the i.ni.d. noise model. Furthermore, we consider and describe two
methods which enhance the performance of planar codes under i.ni.d. noise. The
first method involves a so-called re-weighting process of the conventional
minimum weight perfect matching (MWPM) decoder, while the second one exploits
the relationship that exists between code performance and qubit arrangement in
the surface code lattice. The optimum qubit configuration derived through the
combination of the previous two methods can yield planar code pseudo-threshold
values that are up to $650\%$ higher than for the traditional MWPM decoder
under i.ni.d. noise.
Antonio deMarti iOlius Josu Etxezarreta Martinez Patricio Fuentes Pedro M. Crespo Javier Garcia-Frias