Limitations to the performance of a quantum computer arising from direct interaction between qubits are considered, and the basic scaling laws (with the computation time and the number of qubits) are established for the specific example of the quantum Fourier transform algorithm. These results should be relevant for several of the currently proposed quantum computer systems, where the dominant interaction is of the magnetic dipole-dipole type, in the limit of many qubits and long computation times.

• Received 11 August 1997

DOI:https://doi.org/10.1103/PhysRevA.57.R1