Optimal Universal Quantum Encoding for Statistical Inference
This work addresses the challenge of efficient data encoding for quantum statistical inference, which is incremental as it builds on existing quantum information theory to propose a universal measure and optimal strategies.
The paper tackles the problem of optimally encoding classical data for statistical inference in quantum computing by seeking a universal encoder that works across various tasks, proving that accuracy is bounded by maximal quantum leakage and that pure states and basis encoding are optimal under certain conditions.
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.