NISQRC in a Flexible Qubit-Bus Architecture 2: A Numerical Analysis of Sample-efficient Inference of Non-local Observables

We discuss a generalization of the NISQRC framework [1,2] to sample-efficient machine learning on quantum data, and an architecture for its implementation using an array of transmon qubits coupled to a common flux-tunable bus resonator. A numerical study is presented for the efficacy of this approach to the task of extracting non-local observables on a subset of the qubits coupled to the bus, a notoriously expensive task requiring exponential resources even with state of the art methods. The system evolution is driven by uncalibrated qubit drives and all-to-all coupling, which map the quantum input data to a high-dimensional Hilbert space generating a complex entangling feature map which aids the extraction of non-local information. The bus additionally provides a collective dispersive readout channel from which we study two measurement schemes to extract a collection of measured features based on the readout drive strength: continuous weak measurement (many noisy features) and single strong measurement (few robust features). We show that an optimal basis of noisy features constructed through Eigentask Learning [1] allows us to perform tomographic tasks with fewer measurement resources than purely classical processing approaches.

[1] Hu et al, Phys. Rev. X 13, 041020 (2022)

[2] Hu et al, Nat Commun 15, 7491 (2024)