We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum computation are unstable with respect to the physical realization of the quantum computer. We discuss the origin of these instabilities and discuss possibilities to overcome this, for practical purposes, fundamental limitation of quantum computers.

PACS numbers: 03.67.Lx, 05.30.--d, 89.80.+h, 02.70.Lq