Optimizing continuous dynamical decoupling with machine learning

Decoherence of a quantum system is one of the main difficulties for quantum information processing. Continuous dynamical decoupling has achieved great success in the improvement of the coherence of a quantum state but is difficult to optimize. Here we exploit the black-box optimization process in a machine learning algorithm to optimize the dynamical decoupling scheme. By applying the discrete optimization process to continuous driving fields, we achieve a longer coherence time in comparison to representative schemes of dynamical decoupling. Our black-box-optimization-based machine learning algorithm provides a general routine to tackle the challenging task of improving the coherence of a quantum state for which the dephasing of the system is crucial for operation.

Figure 1

(a) Discretization of the ML algorithm for driving fields. The detunings of the driving fields are discretized into sequences. (b) Schematic showing the key process of our algorithm. The detuning sequences iteratively adjust themselves until the coherence time stops getting improvement.

Figure 2

Continuous-DD performance with different schemes. (a) Rabi oscillation of the two-level system under a single constant driving field. (b) Rabi oscillation obtained with different continuous-DD schemes, marked with different colors: second-order CCD (black), fourth-order CCD (purple), Pulsed DD with CPMG (orange), TDCDD (green), CWDD (blue), and our optimized DD (red). The decoherence rate $\gamma$ is shown in the top right corner of each panel. (c) The optimized detuning sequence values of the driving fields obtained with our ML algorithm. The labels “$i\mathrm{th}$ detuning ${\omega }_i^{\left(\text{A}\right)}$” and “$j\mathrm{th}$ detuning ${\omega }_j^{\left(\text{B}\right)}$” represent the $i\mathrm{th}$ and $j\mathrm{th}$ detuning within the detuning sequence period of the driving field A and B, respectively.

Figure 3

Rabi oscillation of different DD schemes in 50 $\mathrm{\mu s}$. The decoherence process of the Rabi oscillation obtained with our optimized continuous-DD schemes is plotted with red triangles. The dephasing envelopes of the Rabi oscillation under the other five DD schemes are presented with different colors and symbols: second-order CCD, black open circles; fourth-order CCD, purple filled circles; pulsed DD with CPMG, orange diamonds; TDCDD, green crosses; CWDD, blue open squares.

Figure 4

Rabi oscillation envelopes of various DD schemes for different parameter sets. The values of ${\mathrm{\Omega }}_{\text{D1}}$ are as follows: (a) 20, (b) 30, and (c) 50 $\mathrm{M}\mathrm{Hz}$. Curve colors and symbols for the Rabi oscillation envelopes of the six different DD schemes are as in Fig. 3. The fitting decoherence rates $\gamma$ of five of the DD schemes (fourth-order CCD, pulsed DD with CPMG, CWDD, TDCDD, and our optimized DD scheme) are listed in Table 1. Note that the $\gamma$ of the second-order CCD is not presented in the table because the decoherence envelope of the second-order CCD is not suitable for exponential fitting, as mentioned in Sec. 4.