  We report the pressure (p_max = 1.5 GPa) evolution of the crystal structure
of the Weyl semimetal T_d-MoTe_2 by means of neutron diffraction experiments.
We find that the fundamental non-centrosymmetric structure T_d is fully
suppressed and transforms into a centrosymmertic 1T' structure at a critical
pressure of p_cr = 1.2 GPa. This is strong evidence for a pressure induced
quantum phase transition (QPT) between topological to a trivial electronic
state. Although the topological QPT has strong effect on magnetoresistance, it
is interesting that the superconducting critical temperature T_c, the
superfluid density, and the SC gap all change smoothly and continuously across
p_cr and no sudden effects are seen concomitantly with the suppression of the
T_d structure. This implies that the T_c, and thus the SC pairing strength, is
unaffected by the topological QPT. However, the QPT requires the change in the
SC gap symmetry from non-trivial s+- to a trivial s++ state, which we discuss
in this work. Our systematic characterizations of the structure and
superconducting properties associated with the topological QPT provide deep
insight into the pressure induced phase diagram in this topological quantum
material.
