Figure 1

Sequence of gates for the 10-qubit pseudocat-state preparation followed by its decoding into a 10-qubit pseudopure state. The initial preparation of the qutrit into a pseudopure state, as well as the refocusing gates, are not shown. Proper cycling of the $Z$ rotations and the phase of observation act as a coherence filter. The qubit names correspond to the histidine molecule nuclei (see Fig. 2). (a) After the qutrit pseudopure preparation, the state of the register is ${\mathbf{0}}^{{\mathrm{H}}_{4/5}}{\mathbf{I}}^{{\mathrm{H}}_1}{\mathbf{I}}^{{\mathrm{C}}_6}{\mathbf{I}}^{{\mathrm{N}}_2}{\mathbf{I}}^{{\mathrm{H}}_2}{\mathbf{I}}^{{\mathrm{C}}_5}{\mathbf{I}}^{{\mathrm{C}}_4}{\mathbf{Z}}^{{\mathrm{C}}_3}{\mathbf{I}}^{{\mathrm{C}}_2}{\mathbf{I}}^{{\mathrm{H}}_3}{\mathbf{I}}^{{\mathrm{C}}_1}$. At the end of the encoding in (b), it is $\mathbf{0}\mathbf{X}\mathbf{X}\mathbf{X}\mathbf{X}\mathbf{X}\mathbf{X}\mathbf{X}\mathbf{X}\mathbf{X}\mathbf{X}$, and, after filtering, the decoded state in (c) is $\mathbf{0000}\mathbf{X}\mathbf{000000}$.Reuse & Permissions

Figure 2

This $l$-histidine molecule has 14 spin-$1/2$ nuclei: five ${}^1\mathrm{H}$, six ${}^{13}\mathrm{C}$, and three ${}^{15}\mathrm{N}$. See Ref. 24 for a more complete description of the molecule. The two protons ${\mathrm{H}}_4$ and ${\mathrm{H}}_5$, are chemically equivalent and indistinguishable. As such, they can be seen as a composite particle with a spin-1 and a spin-0 part. We considered only the spin-1 subspace (qutrit) since the spin-0 does not interact with the other spin-$1/2$. This molecule is therefore a 12-qubits plus one qutrit quantum register. However, the ${\mathrm{N}}_3$ nuclear spin has a particularly weak coupling with the rest of the molecule; thus, we did not use it. On this plot, we have shown a reference spectrum of ${\mathrm{H}}_2$ (gray plot) and of the pseudopure state obtained after decoding a 10-qubit cat state onto ${\mathrm{H}}_2$ (red line). They are arbitrarily scaled for clarity. The reference spectrum was obtained with 2 scans and the pseudopure, with 4000 scans, in order to improve the signal to noise ratio. We also show simulated spectra of the expected reference (yellow plot) and pseudopure state (blue line) for which the amplitude is matched to the experimental data to evaluate the signal loss.Reuse & Permissions

Figure 3

Description of each of the multiple-coherence experiments. The picture shows how the polarization of the ${\mathrm{H}}_{4/5}$ is propagated through the nuclei chain to create the cat state. In the series of experiments using simple pulses, we first prepared the qutrit made of the two equivalent protons into a pseudopure state $\mathbf{0}=(\mathbf{I}+\mathbf{Z})/2$ and left it as such for the rest of the experiments. When using strongly modulating pulses, we included the qutrit into the multiple-coherence state. The two first and two last columns show the coherence number we reached and how much signal we were able to retain after decoding the cat state into a observable pseudopure state. Results are shown in percentage of the expected signal assuming perfect control, normalized to the first experiment.Reuse & Permissions

Figure 4

Expected decay of the pseudopure state signal due to transversal relaxation for the series of experiments done with simple pulses. Each point corresponds to a different coherence experiment. The length of the pulse sequence increases with the coherence order. Most experimental points are above the estimates given by $T_2^{*}$ and even $T_2$. Indeed, to predict the transversal relaxation during the pulse sequence, we used only a very simple model of decay for multiple coherences that gives an upper bound of the signal loss. Nevertheless, the experimental curve and predicted ones show the same decay pattern. Thus, it is reasonable to say that most of the signal loss comes from decoherence and, therefore, that we have a good operational control over the system. For the coherences 8, 9, and 10 (last three points), the experimental curve goes below the $T_2$ curve. It reflects a loss of accuracy in our operational control. Indeed, for these experiments, we are controlling the nitrogen nuclei through very small couplings. We are, therefore, using long 2-qubits gates that are sensitive to any small inaccuracy in the values of the Hamiltonian parameters.Reuse & Permissions