Optimal Universal Quantum Encoding for Statistical Inference (2404.08172v1)
Abstract: Optimal encoding of classical data for statistical inference using quantum computing is investigated. A universal encoder is sought that is optimal for a wide array of statistical inference tasks. Accuracy of any statistical inference is shown to be upper bounded by a term that is proportional to maximal quantum leakage from the classical data, i.e., the input to the inference model, through its quantum encoding. This demonstrates that the maximal quantum leakage is a universal measure of the quality of the encoding strategy for statistical inference as it only depends on the quantum encoding of the data and not the inference task itself. The optimal universal encoding strategy, i.e., the encoding strategy that maximizes the maximal quantum leakage, is proved to be attained by pure states. When there are enough qubits, basis encoding is proved to be universally optimal. An iterative method for numerically computing the optimal universal encoding strategy is presented.
- M. Schuld, R. Sweke, and J. J. Meyer, Effect of data encoding on the expressive power of variational quantum-machine-learning models, Phys. Rev. A 103, 032430 (2021).
- C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, Theoretical computer science 560, 7 (2014).
- H. L. Haselgrove, Optimal state encoding for quantum walks and quantum communication over spin systems, Physical Review A 72, 062326 (2005).
- N. Elron and Y. C. Eldar, Optimal encoding of classical information in a quantum medium, IEEE transactions on information theory 53, 1900 (2007).
- A. Mitra and P. Mandayam, On optimal cloning and incompatibility, Journal of Physics A: Mathematical and Theoretical 54, 405303 (2021).
- F. Farokhi and S. Kim, Measuring quantum information leakage under detection threat, arXiv preprint arXiv:2403.11433 (2024).
- M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
- M. Wilde, Quantum Information Theory, Quantum Information Theory (Cambridge University Press, 2013).
- F. Farokhi, Maximal information leakage from quantum encoding of classical data, Phys. Rev. A 109, 022608 (2024).
- Z. Denkowski, S. Migórski, and N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Theory, An Introduction to Nonlinear Analysis (Kluwer Academic Publishers, 2003).
- H. Bauer, Minimalstellen von funktionen und extremalpunkte, Archiv der Mathematik 9, 389 (1958).
- W. Sun and Y. X. Yuan, Optimization Theory and Methods: Nonlinear Programming, Springer Optimization and Its Applications (Springer US, 2006).
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