Recently significant progress has been made in (2+1)-dimensional conformal field theories without supersymmetry. In particular, it was realized that different field theory Lagrangians may be related by hidden dualities, i.e., seemingly different Lagrangians may actually be identical in the infrared limit. Among all the proposed dualities, one is particularly relevant in the field of strongly-correlated systems: the one relating the easy-plane noncompact CP^1 model (NCCP^1) and noncompact quantum electrodynamics (QED) with two flavors (N = 2) of massless two-component Dirac fermions. The easy-plane NCCP^1 model is the field theory for the putative deconfined quantum-critical point separating a planar (XY) antiferromagnet and a dimerized (valence-bond solid) ground state, while N=2 noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work we present strong numerical support for the proposed duality. We realize the N=2 noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Also, using stochastic series expansion QMC, we study a planer version of the S=1/2 J-Q spin Hamiltonian (a quantum XY-model model with additional multi-spin couplings) and show that it hosts a continuous transition between the planar magnet and the valence-bound solid. The critical exponents extracted from these two models are in good agreement with the prediction based on the proposed duality.