  The deconfined quantum critical point (DQCP) is an example of phase
transitions beyond the Landau symmetry breaking paradigm that attracts wide
interest. However, its nature has not been settled after decades of study. In
this paper, we apply the recently proposed fuzzy sphere regularization to study
the $\mathrm{SO}(5)$ non-linear sigma model (NL$\sigma$M) with a topological
Wess-Zumino-Witten term, which serves as a dual description of the DQCP with an
exact $\mathrm{SO}(5)$ symmetry. We demonstrate that the fuzzy sphere functions
as a powerful microscope, magnifying and revealing a wealth of crucial
information about the DQCP, ultimately paving the way towards its final answer.
In particular, through exact diagonalization, we provide clear evidence that
the DQCP exhibits approximate conformal symmetry. The evidence includes the
existence of a conserved $\mathrm{SO}(5)$ symmetry current, a stress tensor,
and integer-spaced levels between conformal primaries and their descendants.
Most remarkably, we have identified 23 primaries and 76 conformal descendants.
Furthermore, by examining the renormalization group flow of the lowest symmetry
singlet as well as other primaries, we provide numerical evidence in favour of
DQCP being pseudo-critical, with the approximate conformal symmetry plausibly
emerging from nearby complex fixed points. The primary spectrum we compute also
has important implications, including the conclusion that the $\mathrm{SO}(5)$
DQCP cannot describe a direct transition from the N\'eel to valence bond solid
phase on the honeycomb lattice.
