Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks that could have benefits for near-term devices. The result is a unified framework where classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubitefficient schemes where, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a optimization procedure that could be carried out on quantum hardware, and testing the noise resilience of the trained model.

Processing in Memory (PIM) is a computing paradigm that promises enormous gain in processing speed by eradicating latencies in the typical von Neumann architecture. It has gained popularity owing to its throughput by embedding storage and computation of data in a single unit. We portray implementation of Akers array architecture endowed with PIM computation using Quantum-dot Cellular Automata (QCA). We present the proof of concept of PIM with its realization in the QCA designer paradigm. We illustrate implementation of Ex-OR gate with the help of QCA based Akers Array and put forth many interesting potential possibilities.

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