  Because of a formal equivalence with the partition function of an Ising
chain, the semiclassical traces of the quantum baker map can be calculated
using the transfer-matrix method. We analyze the transfer matrices associated
with the baker map and the symmetry-reflected baker map (the latter happens to
be unitary but the former is not). In both cases simple quantum-circuit
representations are obtained, which exhibit the typical structure of qubit
quantum bakers. In the case of the baker map it is shown that nonunitarity is
restricted to a one-qubit operator (close to a Hadamard gate for some parameter
values). In a suitable continuum limit we recover the already known
infinite-dimensional transfer-operator. We devise truncation schemes allowing
the calculation of long-time traces in regimes where the direct summation of
Gutzwiller's formula is impossible. Some aspects of the long-time divergence of
the semiclassical traces are also discussed.
