Engineered decoherence: Characterization and suppression

Due to omnipresent environmental interferences, quantum coherences inevitably undergo irreversible transformations over certain time scales, thus leading to the loss of encoded information. This process, known as decoherence, has been a major obstacle in realizing efficient quantum information processors. Understanding the mechanism of decoherence is crucial in developing tools to inhibit it. Here we utilize a method proposed by Teklemariam et al. [Phys. Rev. A 67, 062316 (2003)] to engineer artificial decoherence in the system qubits by randomly perturbing their surrounding ancilla qubits. Using a two-qubit nuclear magnetic resonance quantum register, we characterize the artificial decoherence by noise spectroscopy and quantum process tomography. Further, we study the efficacy of dynamical decoupling sequences in suppressing the artificial decoherence. Here we describe the experimental results and their comparisons with theoretical simulations.

Figure 1

The molecular structure of ${}^{13}\mathrm{CHCl}$${}_3$ forming a two-qubit NMR quantum register. The chemical shifts (diagonal elements) and strength of $J$ coupling (off-diagonal element) are shown in the table above. The last two columns indicate relaxation time constants $T_1$ and $T_2$ ($T_2$ was measured using a CPMG sequence with $\tau =3.6$ ms).

Figure 2

Pulse sequences for (a) only kicks, (b) CPMG, (c) seven-pulse UDD, (d) kicks with CPMG, and (e) kicks with UDD. The kicks applied on the environment qubit (${}^{13}\mathrm{C}$) are shown by thin, short vertical lines, and the DD $\pi$ pulses on the system qubit (${}^1\mathrm{H}$) are shown by filled rectangles. The time instants of $\pi$ pulses for the first cycle of duration $t_c=7\tau$ are shown. In the case of UDD [(c) and (e)], exact time instants are calculated from Eq. (8).

Figure 3

Logarithm of transverse magnetization $log\left(M_x\right)$ as a function of time under different pulse sequences as indicated in the legend. Here $\tau =3.2$ ms, $\Gamma =25$ kicks/ms, and $\epsilon \in [0^{\circ },1^{\circ }]$. The $T_2$ values for various pulse sequences are shown in the legend.

Figure 4

Experimental spectral density profiles with different kick angles (as indicated in the legend) and with kick rates 50 kicks/ms (top trace) and 25 kicks/ms (bottom trace). In both the traces, experimental spectral density profile without kicks is also shown for comparison. The smooth lines correspond to empirical fits with one or two Gaussians.

Figure 5

The experimental spectral density (dots) with kick rate $\Gamma =25$ kicks/ms and kick angles $\epsilon \in [0^{\circ },2^{\circ }]$. Theoretical spectral density simulated from Teklemariam's model for the same kick parameters is shown by a smooth line.

Figure 6

The $ZZ$ components of experimental $\left|\chi \right|$ matrices obtained under kicks (K), UDD with kicks ($\text{U}+\text{K}$), and CPMG with kicks ($\text{C}+\text{K}$) are shown in the lower bar plots. In both CPMG and UDD, the cycle time is set to $t_c=7\tau =28$ ms. Corresponding experimental spectral densities $S\left({\omega }_0\right)$ (where ${\omega }_0=\pi /\tau =785\mathrm{rad}/\mathrm{s})$ and other kick parameters are as indicated in the figure. Full $\left|\chi \right|$ matrices for a particular case (as indicated by the arrows) along with the noop case, are shown in the upper trace.