DECOHERENCE LIMITS TO QUANTUM COMPUTATION USING TRAPPED IONS

We investigate the problem of factorization of large numbers on a quan tum computer which ive imagine to be realized within a linear ion trap . Mie derive upper bounds on the size of the numbers that can be facto rized on such a quantum computer. These upper bounds are independent o f the power of the applied laser. We investigate two possible ways to implement qubits, in metastable optical transitions and in Zeeman subl evels of a stable ground state, and show that in both cases the number s that can be factorized are not large enough to be of practical inter est. We also investigate the effect of quantum error correction on our estimates and show that in realistic systems the impact of quantum er ror correction is much smaller than expected. Again no number of pract ical interest can be factorized.