A Hybrid Quantum-Classical System Using Tensor Networks and Variational Quantum Circuits
Great advances have been made to quantum computing in recent years. However, an issue keenly felt by many current quantum system designs is the limited number of quantum bits (qubits) available on current and near-term quantum devices. This greatly limits the dimensionality of data that can be processed using quantum computers. Even as the number of available qubits increases, there would still be an issue as the increase in qubits would cause an exponential increase in the computational complexity of quantum systems. Therefore, there is a strong need to make efficient use of qubits to mitigate both the current limitations in memory and the increases in computational complexity as systems scale up in the future. To this end, a hybrid classical-quantum system is proposed in which a classical tensor network is used on classical data for compression/feature extraction to allow higher-dimensional data to be encoded onto quantum circuits that are practical on current and near-term quantum devices. A quantum-state-fidelity-based loss function is employed to train the network. The quantum part of the hybrid system is based on the QuClassi system proposed by Stein et al. Additionally, the tensor network is analogous to a quantum circuit. This would allow the classical tensor network system to be more easily converted to quantum circuits as more quantum resources become available in the future. This fact, in addition to the the tensor network being trainable, give the tensor network great advantages over Principal Component Analysis (PCA). Using the tensor network as a feature extractor, higher accuracies were achieved while using fewer quantum parameters and qubits for both binary and multi-class classification when compared to QuClassi with PCA.
L'Abbate, Ryan, "A Hybrid Quantum-Classical System Using Tensor Networks and Variational Quantum Circuits" (2022). ETD Collection for Fordham University. AAI29206258.