Long-lived photon-stimulated conductance changes in solid-state materials can enable optical memory and brain-inspired neuromorphic information processing. It remains challenging to realize optical switching with low-energy consumption, and new mechanisms and design principles giving rise to persistent photoconductivity (PPC) can help overcome an important technological hurdle. Here, we demonstrate versatile heterojunctions between metal-halide perovskite nanocrystals and semiconducting single-walled carbon nanotubes that enable room-temperature, long-lived (thousands of seconds), writable, and erasable PPC. Optical switching and basic neuromorphic functions can be stimulated at low operating voltages with femto- to pico-joule energies per spiking event, and detailed analysis demonstrates that PPC in this nanoscale interface arises from field-assisted control of ion migration within the nanocrystal array. Contactless optical measurements also suggest these systems as potential candidates for photonic synapses that are stimulated and read in the optical domain. The tunability of PPC shown here holds promise for neuromorphic computing and other technologies that use optical memory.