= Dynamical decoupling
\b[Dynamical decoupling] applies a designed sequence of control operations to a <quantum system> to suppress unwanted evolution, especially coupling to an environment that causes <quantum decoherence>. The controls repeatedly change how the unwanted interaction acts, so its effects can average away over a cycle. This does not mean that all noise is removed or that arbitrary useful dynamics are automatically preserved.<Experimental realization of robust dynamical decoupling with bounded controls in a solid-state spin system by F. Wang and others>[Introduction: slow environmental coupling and bounded controls]{ref}
For a simple example, let a <qubit> have an unwanted constant <Quantum Hamiltonian> $H=\hbar\Delta Z/2$, where $Z$ is the <Pauli Z gate> matrix. Free evolution for time $\tau$ gives $U(\tau)=e^{-i\Delta\tau Z/2}$. An ideal <Pauli X gate> obeys $XZX=-Z$, hence
$$
XU(\tau)XU(\tau)=e^{+i\Delta\tau Z/2}e^{-i\Delta\tau Z/2}=I.
$$
The two intervals cancel the same constant phase drift in this ideal model. This is the basic refocusing idea behind a <spin echo>. A changing drift, finite pulse duration or imperfect rotation can leave residual error.
A2016 solid-state experiment used <nitrogen-vacancy centers> in <diamond> to compare decoupling protocols with bounded, finite-duration controls. Long shaped control paths were tested against imposed dephasing and more general noise. The experiment matters because instantaneous perfect pulses are an idealization: a useful sequence must account for the control apparatus as well as the unwanted interaction.<Experimental realization of robust dynamical decoupling with bounded controls in a solid-state spin system by F. Wang and others>[Abstract, Introduction and experimental Results: finite-width Eulerian control in NV-center spins]{ref}
Back to article page
