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No Free Lunch for Quantum Machine Learning
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No Free Lunch for Quantum Machine Learning
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The ultimate limits for the quantum machine learning of quantum data are investigated by obtaining a generalisation of the celebrated No Free Lunch (NFL) theorem. We find a lower bound on the quantum risk (the probability that a trained hypothesis is incorrect when presented with a random input) of a quantum learning algorithm trained via pairs of input and output states when averaged over training pairs and unitaries. The bound is illustrated using a recently introduced QNN architecture.
Forward citations
Cited by 3 Pith papers
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No Reference-Free Generalization in Quantum Machine Learning
Without reference information, supervised quantum classifiers are forced to output the same label for every state orthogonal to the training span.
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Measurement-based quantum machine learning
The authors introduce MuTA as a universal quantum neural network for MBQC and numerically demonstrate its ability to learn gates, classify quantum states, and process data under noise, including photonic hardware constraints.
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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, ...
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