Neuromorphic computing has shown remarkable capabilities in silicon-based artificial intelligence, which can be optimized by using Mott materials for functional synaptic connections. However, the research efforts focus on two-terminal artificial synapses and envisioned the networks controlled by silicon-based circuits, which is difficult to develop and integrate. Here, we propose a dynamic network with laser-controlled conducting filaments based on electric field-induced local insulator-metal transition of vanadium dioxide. Quantum sensing is used to realize conductivity-sensitive imaging of conducting filament. We find that the location of filament formation is manipulated by focused laser, which is applicable to simulate the dynamical synaptic connections between the neurons. The ability to process signals with both long-term and short-term potentiation is further demonstrated with ~60 times on/off ratio while switching the pathways. This study opens the door to the development of dynamic network structures depending on easily controlled conduction pathways, mimicking the biological nervous systems.