  The quantum extension of classical finite elements, referred to as quantum
finite elements ({\bf QFE})~\cite{Brower:2018szu,Brower:2016vsl}, is applied to
the radial quantization of 3d $\phi^4$ theory on a simplicial lattice for the
$\mathbb R \times \mathbb S^2$ manifold. Explicit counter terms to cancel the
one- and two-loop ultraviolet defects are implemented to reach the quantum
continuum theory. Using the Brower-Tamayo~\cite{Brower:1989mt} cluster Monte
Carlo algorithm, numerical results support the QFE ansatz that the critical
conformal field theory (CFT) is reached in the continuum with the full
isometries of $\mathbb R \times \mathbb S^2$ restored. The Ricci curvature
term, while technically irrelevant in the quantum theory, is shown to
dramatically improve the convergence opening, the way for high precision Monte
Carlo simulation to determine the CFT data: operator dimensions, trilinear OPE
couplings and the central charge.
