From Bits to Qubits: The Theory and Practice of Quantum Data Encoding

Abstract:Encoding classical data into quantum systems is a foundational step in the execution of nearly all quantum algorithms, and a critical bottleneck in realizing practical quantum advantage. This review provides a comprehensive account of the concepts, algorithms, and practical considerations associated with quantum data encoding. We trace the development from its early conceptual foundations to recent advances, considering commonly used access models, such as quantum state preparation, unitary synthesis, QRAM and block encoding. We survey the circuit size, depth, space-time tradeoffs, as well as non-Clifford resources required for fault-tolerant implementation. We also discuss the roles of different access models in quantum algorithms. Special attention is given to structured data, such as sparse data, Boolean functions and data represented by tensor networks. This review bridges theory and applications, serving both as a pedagogical guide for newcomers and as a reference for active researchers. We also highlight the pivotal role of quantum data encoding in quantum computing and provide insights into future directions that will enable quantum advantage.

Quantum Physics (quant-ph); Computational Physics (physics.comp-ph)

arXiv:2609.08058 [quant-ph]

(or arXiv:2609.08058v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.08058 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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