Compared with the biological paradigms of classical conditioning,non-adaptive computational models are not capable of realistically simulating the biological behavioural functions of the hippocampal regions,because of their implausible requirement for a large number of learning trials,which can be on the order of hundreds.Additionally,these models did not attain a unified,final stable state even after hundreds of learning trials.Conversely,the output response has a different threshold for similar tasks in various models with prolonged transient response of unspecified status via the training or even testing phases.Moreover,most existing cortico-hippocampal computational models use different artificial neural network topologies.These conventional approaches,which simulate various biological paradigms,can get slow training and inadequate conditioned responses for two reasons: in-creases in the number of conditioned stimuli and in the complexity of the simulated biological paradigms in different phases.Additionally,many current computational models that aim to simulate cortical and hippocampal modules of the brain depend on artificial neural networks.However,such classical or even deep neural networks are very slow,sometimes taking thou-sands of trials to obtain the final response with a considerable amount of error.The need for a large number of trials at learning and the inaccurate output responses are due to the complexity of the input cue and the biological processes being simulated.Accordingly,in order to overcome the limitations of the previous proposed computational models,we proposed three models with different aspects to get precise and efficient results.Firstly,the green model which is a combination of adaptive neuro-computational hippocampal and cortical models that is proposed by adaptively updating the whole weights in all layers for both intact networks and lesion networks using instar and outstar learning rules with adaptive resonance theory（ART）.The green model sustains and expands the classical conditioning biological paradigms of the non-adaptive models.The model also overcomes the irregular output response behaviour by using the proposed feature of adaptivity.Further,the model successfully simulates the hip-pocampal regions without passing the final output response back to the whole network,which is considered to be biologically implausible.The results of the Green model showed a signif-icant improvement confirmed by empirical studies of different tasks.In addition,the results indicated that the model outperforms the previously published models.All the obtained results successfully and quickly attained a stable,desired final state（with a unified concluding state of either “1” or “0”）with a significantly shorter transient duration.Practically,all the proposed tasks can be performed in the Green model better than all previous models.Subsequently,the Green model performs successfully with a concise time and active response.However,the computational results are consistent with the compared empirical studies.Secondly,the cortico-hippocampal computational quantum（CHCQ）model which is pro-posed for modeling intact and lesioned systems.The CHCQ model is the first computational model that uses the quantum neural networks for simulating the biological paradigms.The model consists of two entangled quantum neural networks: an adaptive single-layer feedfor-ward quantum neural network and an autoencoder quantum neural network.The CHCQ model adaptively updates all the weights of its quantum neural networks using quantum instar,outstar,and Widrow–Hoff learning algorithms.Our model successfully simulated several biological processes and maintained the output-conditioned responses quickly and efficiently.Moreover,the results were consistent with prior biological studies.However,the results presented notable enhancements approved by experimental studies for various tasks that outperform the previously published models.The results of the CHCQ model has a fast and reliable output responses and reached the final desired states directly after fewer trials than were needed by previous models.The output response of the simulated tasks yielded the desired responses quickly and efficiently compared with other computational models,including the Green model.Thirdly,the computational model for an intact and a lesioned cortico-hippocampal system using quantum-inspired neural networks.This cortico-hippocampal computational quantum-inspired（CHCQI）model simulates cortical and hippocampal modules by using adaptively up-dated neural networks entangled with quantum circuits.The proposed model is used to simulate various classical conditioning tasks related to biological processes.In the CHCQI model,the intact system comprises cortical and hippocampal modules that connect to the same input from the quantum circuit.The lesioned model has the same structure,but the link that forwards the internal representations.The CHCQI model successfully produced the desired outputs of all the simulated tasks with a consistent output responses for intact and lesioned systems.Moreover,in nearly all the tasks,the lesioned system completed the learning faster than the intact system.