Quantum error correction of systematic errors using a quantum search framework

Composite pulses are a quantum control technique for canceling out systematic control errors. We present a different composite pulse sequence inspired by quantum search. Our technique can correct a wider variety of systematic errors—including, for example, nonlinear over-rotational errors—than previous techniques. Concatenation of the pulse sequence can reduce a systematic error to an arbitrarily small level.

Figure 1

Looking down along the vector $\mid s⟩$, the top diagram shows why when $⟨t\mid \overline{U}\mid s⟩=⟨s\mid V\mid s⟩$ is close to 1, $⟨t\mid \overline{U}{R}_0(\pi ∕3){\overline{U}}^{†}{R}_t(\pi ∕3)\overline{U}\mid s⟩=⟨s\mid V{R}_0{V}^{†}{R}_{0}V\mid s⟩$ is even closer to 1. The bottom diagram gives similar intuition for a longer pulse sequence.

Figure 2

Infidelity plotted against the base linear over-rotation parameter $ϵ$. Solid line: unprotected $\pi$ pulse. Dashed line: B2 and B4 pulse sequences. Dotted line: $\pi ∕3Y$ correction on the $\pi$ pulse, and concatenated onto a symmetrized B2 (BB1) pulse sequence.