2 research outputs found
An interpretation of Union-Find Decoder on Weighted Graphs
Union-Find (UF) and Minimum-Weight Perfect Matching (MWPM) are popular
decoder designs for surface codes. The former has significantly lower time
complexity than the latter but is considered somewhat inferior, in terms of
decoding accuracy. In this work we present an interpretation of UF decoders
that explains why UF and MWPM decoders perform closely in some cases: the UF
decoder is an approximate implementation of the blossom algorithm used for
MWPM. This interpretation allows a generalization of UF decoders for weighted
decoding graphs and explains why UF decoders achieve high accuracy for certain
surface codes
Scalable Quantum Error Correction for Surface Codes using FPGA
A fault-tolerant quantum computer must decode and correct errors faster than
they appear. The faster errors can be corrected, the more time the computer can
do useful work. The Union-Find (UF) decoder is promising with an average time
complexity slightly higher than . We report a distributed version of
the UF decoder that exploits parallel computing resources for further speedup.
Using an FPGA-based implementation, we empirically show that this distributed
UF decoder has a sublinear average time complexity with regard to , given
parallel computing resources. The decoding time per measurement round
decreases as increases, a first time for a quantum error decoder. The
implementation employs a scalable architecture called Helios that organizes
parallel computing resources into a hybrid tree-grid structure. Using Xilinx's
cycle-accurate simulator, we present cycle-accurate decoding time for up to
15, with the phenomenological noise model with . We are able to
implement up to 7 with a Xilinx ZC106 FPGA, for which an average decoding
time is 120 ns per measurement round. Since the decoding time per measurement
round of Helios decreases with , Helios can decode a surface code of
arbitrarily large without a growing backlog