Frequently, subroutines in quantum computers have the structure
, where
is some unitary transform and
is performing a quantum computation. In this paper we suggest that if, in analogy to spin echoes,
and
can be implemented symmetrically such that
and
have the same
... [Show full abstract] hardware errors on the logical qubit level, a symmetry boost in the fidelity of the combined quantum operation results that in our simulations reaches up to a factor 10. While we find and document this symmetry boost here in the case of Shor's algorithm, we suggest that other quantum algorithms might profit from similar symmetry performance boosts whenever sub-units of the corresponding quantum algorithm can be identified.