Recent studies on memristive materials and technologies have expanded beyond conventional memory elements, driven by their potential application in novel information processing concepts. Among these materials, conductive domain walls in ferroics are especially promising, offering conductive tunability suitable for reconfigurable multi-state devices. However, challenges such as domain stability, time-dependent conductivity, and low current output have impeded progress in the field. Here, we study the graphene/Pb(Zr,Ti)O3/SrRuO3 system, which demonstrates robust domain wall conduction up to 100 nA/μm2 for 2 V bias, while addressing the critical issue of stability of switched domains. The introduction of graphene electrodes enhances low-voltage stochastic domain formation with limited domain expansion that promotes the emergence of multi-domain states. The developed micrometer sized capacitor devices enable electrically programmable multiple distinct conduction states with robust retention combined with high current output and low operation voltage. These features are highly desirable for memristors and mark the significant potential of domain wall electronics for neuromorphic computing.