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The modular multiplication operator, a central subroutine in Shor's factoringalgorithm, is shown to be a coherent superposition of two quantum bakers mapswhen the multiplier is 2. The classical limit of the maps being completelychaotic, it is shown that there exist perturbations that push the modularmultiplication operator into regimes of generic quantum chaos with spectralfluctuations that are those of random matrices. For the initial state ofrelevance to Shor's algorithm we study fidelity decay due to phase and bit-fliperrors in a single qubit and show exponential decay with shoulders at multiplesor half-multiples of the order. A simple model is used to gain someunderstanding of this behavior.

The modular multiplication operator and the quantized bakers maps