Efficient networks for quantum factoring
Abstract
We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory quantum bits (qubits) and the number of operations required to perform factorization, using the algorithm suggested by Shor [in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994), p. 124]. A Kbit number can be factored in time of order K^{3} using a machine capable of storing 5K+1 qubits. Evaluation of the modular exponential function (the bottleneck of Shor's algorithm) could be achieved with about 72K^{3} elementary quantum gates; implementation using a linear ion trap would require about 396K^{3} laser pulses. A proofofprinciple demonstration of quantum factoring (factorization of 15) could be performed with only 6 trapped ions and 38 laser pulses. Though the ion trap may never be a useful computer, it will be a powerful device for exploring experimentally the properties of entangled quantum states.
 Publication:

Physical Review A
 Pub Date:
 August 1996
 DOI:
 10.1103/PhysRevA.54.1034
 arXiv:
 arXiv:quantph/9602016
 Bibcode:
 1996PhRvA..54.1034B
 Keywords:

 03.65.Bz;
 89.80.+h;
 Quantum Physics
 EPrint:
 56 pages, 22 figures, uses REVTeX, epsf