A model of interacting quantum neurons with a dynamic synapse

Motivated by recent advances in neuroscience, in this work, we explore the emergent behaviour of quantum systems with a dynamical biologically-inspired qubits interaction. We use a minimal model of two interacting qubits with an activity-dependent dynamic interplay as in classical dynamic synapses that induces the so-called synaptic depression, that is, synapses that present synaptic fatigue after heavy presynaptic stimulation. Our study shows that in absence of synaptic depression the two-qubits quantum system shows typical Rabi oscillations whose frequency decreases when synaptic depression is introduced, so one can trap excitations for a large period of time. This creates a population imbalance between the qubits even though the Hamiltonian is Hermitian. This imbalance can be sustained in time by introducing a small energy shift between the qubits. In addition, we report that long time entanglement between the two qubits raises naturally in the presence of synaptic depression. Moreover, we propose and analyse a plausible experimental setup of our two-qubits system which demonstrates that these results are robust and can be experimentally obtained in a laboratory.