  In the quantum compression scheme proposed by Schumacher, Alice compresses a
message that Bob decompresses. In that approach, there is some probability of
failure and, even when successful, some distortion of the state. For
sufficiently large blocklengths, both of these imperfections can be made
arbitrarily small while achieving a compression rate that asymptotically
approaches the source coding bound. However, direct implementation of
Schumacher compression suffers from poor circuit complexity. In this paper, we
consider a slightly different approach based on classical syndrome source
coding. The idea is to use a linear error-correcting code and treat the message
to be compressed as an error pattern. If the message is a correctable error
(i.e., a coset leader) then Alice can use the error-correcting code to convert
her message to a corresponding quantum syndrome. An implementation of this
based on polar codes is described and simulated. As in classical source coding
based on polar codes, Alice maps the information into the ``frozen" qubits that
constitute the syndrome. To decompress, Bob utilizes a quantum version of
successive cancellation coding.
