Arbitrarily accurate composite pulse sequences

TLDR

Systematic errors dominate quantum control, but composite pulse sequences—well studied in NMR—can cancel errors by symmetry. The study extends composite pulse techniques to cancel errors to arbitrary order O(ϵⁿ). The authors employ composite pulse sequences that cancel errors by symmetry, extending the method to achieve arbitrary order O(ϵⁿ) cancellation. The technique reduces errors to O(ϵ³) without knowing ϵ and works for any initial state.

Abstract

Systematic errors in quantum operations can be the dominating source of imperfection in achieving control over quantum systems. This problem, which has been well studied in nuclear magnetic resonance, can be addressed by replacing single operations with composite sequences of pulsed operations, which cause errors to cancel by symmetry. Remarkably, this can be achieved without knowledge of the amount of error $ϵ$. Independent of the initial state of the system, current techniques allow the error to be reduced to $O({ϵ}^{3})$. Here, we extend the composite pulse technique to cancel errors to $O({ϵ}^{n})$, for arbitrary $n$.