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Because of a formal equivalence with the partition function of an Isingchain, the semiclassical traces of the quantum baker map can be calculatedusing the transfer-matrix method. We analyze the transfer matrices associatedwith the baker map and the symmetry-reflected baker map (the latter happens tobe unitary but the former is not). In both cases simple quantum-circuitrepresentations are obtained, which exhibit the typical structure of qubitquantum bakers. In the case of the baker map it is shown that nonunitarity isrestricted to a one-qubit operator (close to a Hadamard gate for some parametervalues). In a suitable continuum limit we recover the already knowninfinite-dimensional transfer-operator. We devise truncation schemes allowingthe calculation of long-time traces in regimes where the direct summation ofGutzwiller's formula is impossible. Some aspects of the long-time divergence ofthe semiclassical traces are also discussed.

Transfer matrices and circuit representation for the semiclassical traces of the baker map