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We demonstrate the use of matrix product state (MPS) models fordiscriminating quantum data on quantum computers using holographic algorithms,focusing on classifying a translationally invariant quantum state based on $L$qubits of quantum data extracted from it. We detail a process in which datafrom single-shot experimental measurements are used to optimize an isometrictensor network, the tensors are compiled into unitary quantum operations usinggreedy compilation heuristics, parameter optimization on the resulting quantumcircuit model removes the post-selection requirements of the isometric tensormodel, and the resulting quantum model is inferenced on either product state orentangled quantum data. We demonstrate our training and inference architectureon a synthetic dataset of six-site single-shot measurements from the bulk of aone-dimensional transverse field Ising model (TFIM) deep in itsantiferromagnetic and paramagnetic phases. We experimentally evaluate models onQuantinuum's H1-2 trapped ion quantum computer using entangled input datamodeled as translationally invariant, bond dimension 4 MPSs across the knownquantum phase transition of the TFIM. Using linear regression on theexperimental data near the transition point, we find predictions for thecritical transverse field of $h=0.962$ and $0.994$ for tensor networkdiscriminators of bond dimension $\chi=2$ and $\chi=4$, respectively. Thesepredictions compare favorably with the known transition location of $h=1$despite training on data far from the transition point. Our techniques identifyfamilies of short-depth variational quantum circuits in a data-driven andhardware-aware fashion and robust classical techniques to precondition themodel parameters, and can be adapted beyond machine learning to myriadapplications of tensor networks on quantum computers, such as quantumsimulation and error correction.

A tensor network discriminator architecture for classification of quantum data on quantum computers