Quantum computing offers significant potential for tackling complex problems, yet preparing quantum states from real-world data remains a critical challenge. We introduce the statistics-informed parameterized quantum circuit (SI-PQC), an approach specifically designed to efficiently prepare arbitrary statistical distributions. By leveraging statistical symmetries in data through the maximum entropy principle, SI-PQC encodes prior information with a fixed-structure circuit and tunable parameters, eliminating extensive pre-processing. This method achieves exponential resource savings in preparing mixture models, crucial for applications in statistics and machine learning. SI-PQC also supports variational learning within an optimally dimensioned training space, enhancing generalization, trainability and statistical interpretability. Numerical experiments confirm that SI-PQC can effectively prepare diverse distributions and accurately learn Gaussian mixture models, aligning closely with theoretical expectations. Applications in financial derivatives pricing and online risk analysis showcase SI-PQC’s practical advantages, with substantial improvements in end-to-end quantum resource efficiency and applicability to empirical data. As a versatile and resource-efficient subroutine, SI-PQC broadens the scope of quantum algorithms, especially in real-time, data-driven fields such as finance, online machine learning, and medical diagnostics.

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SI-PQC is a new quantum circuit approach for efficiently preparing quantum states from statistical distributions using the maximum entropy principle. It achieves exponential resource savings for mixture models by encoding statistical symmetries with fixed-structure circuits and tunable parameters, eliminating extensive preprocessing. The method supports variational learning with improved generalization and trainability. Numerical experiments demonstrate effective preparation of diverse distributions and accurate learning of Gaussian mixture models. Applications in financial derivatives pricing and risk analysis show substantial improvements in quantum resource efficiency, making it practical for real-time, data-driven fields like finance, online machine learning, and medical diagnostics.

Statistics-informed parameterized quantum circuit: towards practical quantum state preparation and learning via maximum entropy principle