Noise filtering in nontrivial quantum logic gates
Todd Green, Hermann Uys, Michael J. Biercuk · arXiv (Cornell University) · 2011
Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of non-commuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. The calculation employs physically realistic bounded-strength controls and a filter-design framework to accurately predict error rates due to classical noise, a key capability in quantum information. We derive explicit filter functions for flexible control sequences, and use them to study the performance of dynamically corrected gates. Our analytic calculations -- validated by brute-force numerics -- show that these control sequences can provide many orders of magnitude in error suppression in the presence of Non-Markovian time-varying classical noise.