A Pauli-transfer-matrix analysis of QELMs reveals the full set of nonlinear Pauli features generated by encoding and transformed by quantum channels, producing an interpretable classical nonlinear vector autoregression model that approximates flow maps in dynamical systems.
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The paper proves sample complexity bounds showing that any efficiently representable unitary can be learned incoherently with arbitrary measurements, but only low-entangling unitaries with shallow-depth measurements, and demonstrates this on a 16-qubit hardware device.
Extends Fano bounds to sufficiency of low conditional entropy and defines a quantum entanglement task for infinite-dimensional systems with bounds via maximal singlet fraction of finite-dimensional approximations.
citing papers explorer
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Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approach
A Pauli-transfer-matrix analysis of QELMs reveals the full set of nonlinear Pauli features generated by encoding and transformed by quantum channels, producing an interpretable classical nonlinear vector autoregression model that approximates flow maps in dynamical systems.
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The power and limitations of learning quantum dynamics incoherently
The paper proves sample complexity bounds showing that any efficiently representable unitary can be learned incoherently with arbitrary measurements, but only low-entangling unitaries with shallow-depth measurements, and demonstrates this on a 16-qubit hardware device.
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On the coherent extension of some Fano-type learning bounds
Extends Fano bounds to sufficiency of low conditional entropy and defines a quantum entanglement task for infinite-dimensional systems with bounds via maximal singlet fraction of finite-dimensional approximations.