Error sensitivity of a Quantum Simulator I: a first example

As the first useful Quantum Computers will be quantum simulators, here the minimum number of qubits necessary for the solution of the Schroedinger equation in simple test problems is evaluated. From the present preliminary results it appears that it is possible to realize a useful quantum simulator with a register of only 10-15 qbits. The intrinsic sensitivity to some errors appears to be moderate without the need of error correcting methods. At present there is at least some indication that the amplitude errors are more dangerous than phase and decoherence errors. So corrections limited to amplitude errors may be very useful.