Experimental realization of a quantum image classifier via tensor-network-based machine learning

Quantum machine learning aspires to overcome intractability that currently limits its applicability to practical applications.However,quantum machine learning itself is limited by low effective dimensions achievable in stateof-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.

Thermodynamics of spin-1/2 Kagomé Heisenberg antiferromagnet:algebraic paramagnetic liquid and finite-temperature phase diagram

Quantum fluctuations from frustration can trigger quantum spin liquids(QSLs) at zero temperature.However, it is unclear how thermal fluctuations affect a QSL. We employ state-of-the-art tensor network-based methods to explore the ground state and thermodynamic properties of the spin-1=2 kagomé Heisenberg antiferromagnet(KHA). Its ground state is shown to be consistent with a gapless QSL by observing the absence of zero-magnetization plateau as well as the algebraic behaviors of susceptibility and specific heat at low temperatures, respectively. We show that there exists an algebraic paramagnetic liquid(APL) that possesses both the paramagnetic properties and the algebraic behaviors inherited from the QSL. The APL is induced under the interplay between quantum fluctuations from geometrical frustration and thermal fluctuations. By studying the temperature-dependent behaviors of specific heat and magnetic susceptibility, a finite-temperature phase diagram in a magnetic field is suggested, where various phases are identified. This present study gains useful insight into the thermodynamic properties of the spin-1/2 KHA with or without a magnetic field and is helpful for relevant experimental studies.