Single-bit feedback and quantum-dynamical decoupling

Synthesizing an effective identity evolution in a target system subjected to unwanted unitary or nonunitary dynamics is a fundamental task for both quantum control and quantum information processing applications. Here, we investigate how single-bit, discrete-time feedback capabilities may be exploited to enact or to enhance quantum procedures for effectively suppressing unwanted dynamics in a finite-dimensional open quantum system. An explicit characterization of the joint unitary propagators correctable by a single-bit feedback strategy for arbitrary evolution time is obtained. For a two-dimensional target system, we show how by appropriately combining quantum feedback with dynamical decoupling methods, concatenated feedback-decoupling schemes may be built, which can operate under relaxed control assumptions and can outperform purely closed-loop and open-loop protocols.

Figure 1

(Color online) Comparison between selective DD protocols: FDD (brown, circles) and SELDD, with ${\sigma }_x$ (blue, squares) or ${\sigma }_y$ (green, triangles) pulses. Symbols are displayed every four decoupling cycles to improve readability. Brown and blue curves correspond to oscillations of the form $\mathcal{F}\left(T\right)=\cos {\left({\epsilon }_{x,y}T\right)}^2$, respectively, as follows from Eq. (26) for the selectively decoupled evolution. Actual Hamiltonian, $H={\Omega }_z{\sigma }_z+{\epsilon }_x{\sigma }_x+{\epsilon }_y{\sigma }_y$, ${\epsilon }_x={\Omega }_z∕20$, ${\epsilon }_y={\Omega }_z∕10$. The estimated Hamiltonian is proportional to ${\sigma }_z$. ${\Omega }_z=30$, ${\Omega }_z\Delta t=0.04$.

Figure 2

(Color online) Comparison between maximal DD protocols: MAXDD (blue, squares), symmetrized FED (brown, circles), nonsymmetrized FED (green, triangles), DEF (red, diamonds). Symbols are displayed every two decoupling cycles to improve readability. Actual Hamiltonian: $H={\Omega }_z{\sigma }_z+{\epsilon }_x{\sigma }_x+{\epsilon }_y{\sigma }_y$, ${\epsilon }_x={\epsilon }_y={\Omega }_z∕10$. The estimated Hamiltonian is proportional to ${\sigma }_z$. ${\Omega }_{z}T=120$, ${\Omega }_z\Delta t=0.32$.