Entanglement and coherence dynamics in photonic quantum memristors

Memristive systems exhibit dynamics that depend on their past states, making them useful as memory units. Recently, quantum memristor models have been proposed, and notably, a photonic quantum memristor (PQM) has been experimentally proven. In this work, we explore and characterize various quantum properties that emerge from this specific model of PQM. First, we find that a single PQM displays memristive dynamics on its quantum coherence. Second, we analytically show that a network made of two independent PQMs can manifest memory effects on the dynamics of both entanglement and coherence of correlated photons traveling through the network, regardless of their distance, in the hypothesis of negligible external disturbances. Additionally, we build and run a circuit-model of the PQM on a real qubit-based quantum computer (IBM-Q), showing that (1) this system can effectively be used for nonlinear quantum computing under specific conditions and (2) digital quantum simulations can reproduce the dynamics of a memristive quantum system in a non-Markovian regime.