Quantum chaos and quantum algorithms

It was recently shown (e-print 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.