the slower measurements were made by the extraction method, and the initial relative measurements were adjusted to the absolute value extraction points. The field could be rapidly changed at a rate up to 2.2 T s$^{-1}$.

For all the data shown here the field was applied along the \[111\] crystallographic direction. Measurements were also performed perpendicular to the \[111\] direction, as well as along the \[001\] and \[011\] directions and on a polycrystalline sample, examples of which are discussed in Supplementary Note 3. In total ten different samples were studied. The direction of the applied field as well as differences in the sample shapes and thermal contact with the sample holder can effect some of the details of the measurements. However this does not change the main conclusion of the paper: the demonstration of the importance of nuclear assisted quantum tunnelling to the relaxation.

The measurements of temperature vs time shown in Fig. 2, a bare-chip Cernox 1010-BC resistance thermometer from LakeShore Cryogenics was wrapped in Cu foil and glued on top of the sample as shown in the inset of Fig. 2b.

Cooling [Ho$_{2}$Ti$_{2}$O$_{7}$]{} was difficult and warming was also tricky using the AQP, depending on the initial temperatures 