title: Transfer matrices and circuit representation for the semiclassical traces of the baker map.
abstract: 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.
authors.affiliation: Departamento de Física, Comisión Nacional de Energía Atómica, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina. carlo@tandar.cnea.gov.ar
authors.forename: Gabriel G
authors.initials: GG
authors.lastname: Carlo
authors.forename: Raúl O
authors.initials: RO
authors.lastname: Vallejos
authors.forename: Rômulo F
authors.initials: RF
authors.lastname: Abreu