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Hybrid Quantum-Classical algorithms are a promising candidate for developing uses for NISQ devices. In particular, Parametrised Quantum Circuits (PQCs) paired with classical optimizers have been used as a basis for quantum chemistry and quantum optimization problems. Training PQCs relies on methods to overcome the fact that the gradients of PQCs vanish exponentially in the size of the circuits used. Tensor network methods are being increasingly used as a classical machine learning tool, as well as a tool for studying quantum systems. We introduce a circuit pre-training method based on matrix product state machine learning methods, and demonstrate that it accelerates training of PQCs for both supervised learning, energy minimization, and combinatorial optimization.
In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this connection has
We demonstrate that the optimal states in lossy quantum interferometry may be efficiently simulated using low rank matrix product states. We argue that this should be expected in all realistic quantum metrological protocols with uncorrelated noise an
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states (MPS) are kn
Many quantum machine learning (QML) algorithms that claim speed-up over their classical counterparts only generate quantum states as solutions instead of their final classical description. The additional step to decode quantum states into classical v
Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that machine learning enhanced by quantum computing is closely relat