  It was recently shown (quant-ph/9909074) that parasitic random interactions
between the qubits in a quantum computer can induce quantum chaos and put into
question the operability of a quantum computer. In this work I investigate
whether already the interactions between the qubits introduced with the
intention to operate the quantum computer may lead to quantum chaos. The
analysis focuses on two well--known quantum algorithms, namely Grover's search
algorithm and the quantum Fourier transform. I show that in both cases the same
very unusual combination of signatures from chaotic and from integrable
dynamics arises.
