  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 epsilon. Independent of the initial state of
the system, current techniques allow the error to be reduced to O(epsilon^3).
Here, we extend the composite pulse technique to cancel errors to O(epsilon^n),
for arbitrary n.
