Quantum State Preparation for Classical Data Encoding

• Miguel A. A. Lisboa UFPB
• Victor H. F. Brasil UFPB
• João V. H. Duarte UFPB
• Leandro C. Souza UFPB / Venturus

DOI: https://doi.org/10.5753/sbccq.2026.20984

Resumo

Quantum state preparation is the process of producing a target quantum state that will be used as the input to a quantum circuit. Many quantum algorithms require an input state where amplitudes, phases, or basis probabilities encode problem data, and the cost of preparing this state can be significant in gate count and circuit depth. This review summarizes common goals, assumptions, and methods for quantum state preparation, with emphasis on preparing states from classical vectors, probability distributions, and feature data used in quantum machine learning. We organize approaches by the information they load and by the resources they require, including gate count, circuit depth, qubit overhead, and classical preprocessing. It also compares exact and approximate preparation procedures, and discusses how precision targets affect cost. The review highlights links between families of methods, typical sources of resource estimates, and criteria that help match a preparation method to a task and hardware constraints.

Referências

Benedetti, M., Lloyd, E., Sack, S., and Fiorentini, M. (2019). Parameterized quantum circuits as machine learning models. Quantum Science and Technology, 4(4):043001.

Bennett, C. H. and Wiesner, S. J. (1992). Communication via one- and two-particle operators on einstein-podolsky-rosen states. Physical Review Letters, 69:2881–2884.

Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., and Lloyd, S. (2017). Quantum machine learning. Nature, 549(7671):195–202.

Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., McClean, J. R., Mitarai, K., Yuan, X., Cincio, L., and Coles, P. J. (2021). Variational quantum algorithms. Nature Reviews Physics, 3:625–644.

Dunjko, V. and Briegel, H. J. (2018). Machine learning & artificial intelligence in the quantum domain: a review of recent progress. Reports on Progress in Physics, 81(7):074001.

Giovannetti, V., Lloyd, S., and Maccone, L. (2008a). Architectures for a quantum random access memory. Physical Review A, 78:052310.

Giovannetti, V., Lloyd, S., and Maccone, L. (2008b). Quantum random access memory. Physical Review Letters, 100:160501.

Gosset, D., Kothari, R., and Wu, K. (2026). Quantum state preparation with optimal T-count. In Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society for Industrial and Applied Mathematics.

Grover, L. K. and Rudolph, T. (2002). Creating superpositions that correspond to efficiently integrable probability distributions.

Hur, T., Kim, L., and Park, D. K. (2022). Quantum convolutional neural network for classical data classification. Quantum Machine Intelligence, 4(1):3.

Khan, M. A., Aman, M. N., and Sikdar, B. (2024). Beyond bits: A review of quantum embedding techniques for efficient information processing. IEEE Access, 12:46118–46137.

Lloyd, S. (1996). Universal quantum simulators. Science, 273(5278):1073–1078.

Low, G. H. and Chuang, I. L. (2017). Optimal hamiltonian simulation by quantum signal processing. Physical Review Letters, 118:010501.

Möttönen, M., Vartiainen, J. J., Bergholm, V., and Salomaa, M. M. (2005). Transformation of quantum states using uniformly controlled rotations. Quantum Information & Computation, 5:467–473.

Nielsen, M. A. and Chuang, I. L. (2010). Quantum Computation and Quantum Information. Cambridge University Press.

Preskill, J. (2018). Quantum computing in the nisq era and beyond. Quantum, 2:79.

Rosenkranz, M., Brunner, E., Marin-Sanchez, G., Fitzpatrick, N., Dilkes, S., Tang, Y., Kikuchi, Y., and Benedetti, M. (2025). Quantum state preparation for multivariate functions. Quantum, 9:1703.

Schuld, M., Bocharov, A., Svore, K. M., and Wiebe, N. (2020). Circuit-centric quantum classifiers. Physical Review A, 101:032308.

Schuld, M. and Petruccione, F. (2021). Machine Learning with Quantum Computers. Springer.

Shende, V. V., Bullock, S. S., and Markov, I. L. (2006). Synthesis of quantum-logic circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 25(6):1000–1010.

Soklakov, A. N. and Schack, R. (2006). Efficient state preparation for a register of quantum bits. Physical Review A, 73:012307.

Sun, X., Tian, G., Yang, S., Yuan, P., and Zhang, S. (2023). Asymptotically optimal circuit depth for quantum state preparation and general unitary synthesis. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 42(10):3301–3314.

Zhang, X.-M., Li, T., and Yuan, X. (2022). Quantum state preparation with optimal circuit depth: Implementations and applications. Physical Review Letters, 129(23):230504.