696 research outputs found
Belief propagation decoding of quantum channels by passing quantum messages
Belief propagation is a powerful tool in statistical physics, machine
learning, and modern coding theory. As a decoding method, it is ubiquitous in
classical error correction and has also been applied to stabilizer-based
quantum error correction. The algorithm works by passing messages between nodes
of the factor graph associated with the code and enables efficient decoding, in
some cases even up to the Shannon capacity of the channel. Here we construct a
belief propagation algorithm which passes quantum messages on the factor graph
and is capable of decoding the classical-quantum channel with pure state
outputs. This gives explicit decoding circuits whose number of gates is
quadratic in the blocklength of the code. We also show that this decoder can be
modified to work with polar codes for the pure state channel and as part of a
polar decoder for transmitting quantum information over the amplitude damping
channel. These represent the first explicit capacity-achieving decoders for
non-Pauli channels.Comment: v3: final version for publication; v2: improved discussion of the
algorithm; 7 pages & 2 figures. v1: 6 pages, 1 figur
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