Quantum Machine Learning Matrix Product States
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Matrix product states minimize bipartite correlations to compress the classical data representing quantum states. Matrix product state algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods used to simulate many-body physics. Matrix product states have a further range of applications in machine learning. Finding matrix product states is in general a computationally challenging task, a computational task which we show quantum computers can accelerate. We present a quantum algorithm which returns a classical description of a k-rank matrix product state approximating an eigenvector given black-box access to a unitary matrix. Each iteration of the optimization requires O(n· k^2) quantum gates, yielding sufficient conditions for our quantum variational algorithm to terminate in polynomial-time.
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