arXiv:quant-ph/0603212 · Journal of Physics A Mathematical and General

Quantum baker maps with controlled-not coupling

Raúl O Vallejos, Pedro R del Santoro, Alfredo M Ozorio de Almeida

Published Apr 19, 2006• 4 citations

Abstract

The characteristic stretching and squeezing of chaotic motion is linearized within the finite number of phase space domains which subdivide a classical baker map. Tensor products of such maps are also chaotic, but a more interesting generalized baker map arises if the stacking orders for the factor maps are allowed to interact. These maps are readily quantized, in such a way that the stacking interaction is entirely attributed to primary qubits in each map, if each j th subsystem has Hilbert space dimension . We here study the particular example of two baker maps that interact via a controlled-not interaction, which is a universal gate for quantum computation. Numerical evidence indicates that the control subspace becomes an ideal Markovian environment for the target map in the limit of large Hilbert space dimension.

DOI: 10.1088/0305-4470/39/18/028

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