  Quantum machine learning aspires to overcome intractability that currently
limits its applicability to practical problems. However, quantum machine
learning itself is limited by low effective dimensions achievable in
state-of-the-art experiments. Here we demonstrate highly successful
classifications of real-life images using photonic qubits, combining a quantum
tensor-network representation of hand-written digits and entanglement-based
optimization. Specifically, we focus on binary classification for hand-written
zeroes and ones, whose features are cast into the tensor-network
representation, further reduced by optimization based on entanglement entropy
and encoded into two-qubit photonic states. We then demonstrate image
classification with a high success rate exceeding 98%, through successive gate
operations and projective measurements. Although we work with photons, our
approach is amenable to other physical realizations such as nitrogen-vacancy
centers, nuclear spins and trapped ions, and our scheme can be scaled to
efficient multi-qubit encodings of features in the tensor-product
representation, thereby setting the stage for quantum-enhanced multi-class
classification.
