Figure 1

The proton-decoupled ${}^{13}\mathrm{C}$ spectrum of malonic acid in the orientation used in the experiments. The experiments were performed in a static field of 7.1 T using a purpose-built probe. Also shown is the molecule and a table of the Hamiltonian parameters (kHz). Diagonal elements give chemical shifts with respect to the transmitter frequency (Hamiltonian $\sum _i\pi {\omega }_i{\sigma }_z^i$). Below the diagonal are dipolar couplings ($\sum _{i<j}\frac{\pi }{2}{D}_{ij}(2{\sigma }_z^i{\sigma }_z^j-{\sigma }_x^i{\sigma }_x^j-{\sigma }_y^i{\sigma }_y^j)$) and above are $J$ coupling constants $\sum _{i<j}\frac{\pi }{2}{J}_{ij}({\sigma }_z^i{\sigma }_z^j+{\sigma }_x^i{\sigma }_x^j+{\sigma }_y^i{\sigma }_y^j)$). ${}^{13}\mathrm{C}–{}^{13}\mathrm{C}$ Hamiltonian values are obtained from the spectral fit. The peak heights give information about the relative strengths of the dipolar and the indirect $J$ couplings. The three central peaks of each multiplet are from the natural abundance of ${}^{13}\mathrm{C}$ present in the molecule at $\approx 1\%$. Combining the fitting information with crystal structure data from neutron scattering experiments [31] gives the orientation of the molecule with respect to the static magnetic field and from that the proton-carbon dipolar couplings.Reuse & Permissions

Figure 2

The quantum circuit implemented (see text) with the ideal polarizations noted in terms of the heat-bath polarization $ϵ$. Each set of swap and compression gate is considered a step and the ideal polarization on the target qubit ${\mathrm{C}}_2$ should increase as 1.5, 1.75, 1.88, 1.94 in steps 1 through 4. The refresh operations swap polarization from ${\mathrm{H}}_{m1,2}$ to ${\mathrm{C}}_m$ with a short contact CP. The thermal contact between ${\mathrm{H}}_{m1,2}$ and the rest of the proton bath takes place during the spin-locking decoupling pulse for the duration of the carbon register operations. The swap gates are 1.6 ms and the compression gate 2.2 ms. The compression gate is equivalent to a permutation of the diagonal elements of the density matrix, and one possible implementation is shown decomposed as C-NOT-NOT and Toffoli gates [14]; however, it was implemented as a single GRAPE pulse. The bottom trace shows the amplitude of the radio frequency control fields for the pulse sequence. The inset shows in detail the two quadrature components of one of the GRAPE control pulses which implements a unitary swap gate between qubits 1 and 3.Reuse & Permissions

Figure 3

Table of the measured polarization (with respect to the initial refresh step) of each spin after the compression gates (steps 6, 10, 14, 18 in the PPA). All results are $\pm 0.02$. For the final compression step the heat-bath polarization is no longer needed which allows a switch from the spin-locking cw decoupling to the more efficient SPINAL64 [26] (without the switch the enhancement is $1.67\times$). The spectra show a comparison of the first refresh step (swapped to ${\mathrm{C}}_2$) and the final signal after four compression steps. There is a clear boost of signal on ${\mathrm{C}}_2$, and also substantial polarization on ${\mathrm{C}}_1$ and ${\mathrm{C}}_m$. The distortions in the spectrum evident for ${\mathrm{C}}_1$ and ${\mathrm{C}}_m$ are due to residual natural abundance ${}^{13}\mathrm{C}$ signal.Reuse & Permissions