Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks that could have benefits for near-term devices. The result is a unified framework where classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubitefficient schemes where, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a optimization procedure that could be carried out on quantum hardware, and testing the noise resilience of the trained model.

The axion is a light pseudoscalar particle which suppresses CP-violating effects in strong interactions and also happens to be an excellent dark matter candidate. Axions constituting the dark matter halo of our galaxy may be detected by their resonant conversion to photons in a microwave cavity permeated by a magnetic field. The current generation of the microwave cavity experiment has demonstrated sensitivity to plausible axion models, and upgrades in progress should achieve the sensitivity required for a definitive search, at least for low mass axions. However, a comprehensive strategy for scanning the entire mass range, from 1-1000 µeV, will require significant technological advances to maintain the needed sensitivity at higher frequencies. Such advances could include sub-quantum-limited amplifiers based on squeezed vacuum states, bolometers, and/or superconducting microwave cavities. The Axion Dark Matter eXperiment at High Frequencies (ADMX-HF) represents both a pathfinder for first data in the 20-100 µeV range (∼5-25 GHz), and an innovation test-bed for these concepts.

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Ternary quantum processors offer significant potential computational advantages over conventional qubit technologies, leveraging the encoding and processing of quantum information in qutrits (three-level systems). To evaluate and compare the performance of such emerging quantum hardware it is essential to have robust benchmarking methods suitable for a higher-dimensional Hilbert space. We demonstrate extensions of industry standard randomized benchmarking (RB) protocols, developed and used extensively for qubits, suitable for ternary quantum logic. Using a superconducting five-qutrit processor, we find an average single-qutrit process infidelity of 3.8 × 10 −3 . Through interleaved RB, we characterize a few relevant gates, and employ simultaneous RB to fully characterize crosstalk errors. Finally, we apply cycle benchmarking to a two-qutrit CSUM gate and obtain a two-qutrit process fidelity of 0.85. Our results present and demonstrate RB-based tools to characterize the performance of a qutrit processor, and a general approach to diagnose control errors in future qudit hardware.