Robustness and performance scaling of a quantum computer with respect to a class of static defects

Abstract

Competing computationally with experimental groups for the construction of scaling quantum computers, we simulate a complete quantum-gate by quantum-gate implementation of Shor's algorithm on a classical 128-core cluster computer. The resulting virtual quantum computer serves as a convenient quantum laboratory for the investigation of the effect of defects in the quantum circuitry. The class of defects studied here is the removal of all rotation gates with rotation angles $\ensuremath{\theta}<\ensuremath{\pi}/{2}^{b}$. Factoring semiprimes $N=21,33,35,39,55,57$, we find that the quantum computer still operates with acceptable performance (success probability of factoring) down to $b=2$. This is surprising since the deletion of rotation gates results in large errors in the arithmetic circuitry of the quantum computer. Extrapolating on the basis of these results we conclude that for quantum computers of practical interest more than 99% of rotation gates may be discarded with acceptable consequences in quantum computer performance. This result may be of interest to experimental physicists and quantum engineers currently embarked on designing efficient circuitry for scaling quantum computers.