  We investigate quantum phase transitions in the spin-1/2 Heisenberg
antiferromagnet on square lattices with inhomogeneous bond dilution. It is
shown that quantum fluctuations can be continuously tuned by inhomogeneous bond
dilution, eventually leading to the destruction of long-range magnetic order on
the percolating cluster. Two multicritical points are identified at which the
magnetic transition separates from the percolation transition, introducing a
novel quantum phase transition. Beyond these multicritical points a
quantum-disordered phase appears, characterized by an infinite percolating
cluster with short ranged antiferromagnetic order. In this phase, the
low-temperature uniform susceptibility diverges algebraically with
non-universal exponents. This is a signature that the novel quantum-disordered
phase is a quantum Griffiths phase, as also directly confirmed by the
statistical distribution of local gaps. This study thus presents evidence of a
genuine quantum Griffiths phenomenon in a two-dimensional Heisenberg
antiferromagnet.
