References
- M. A. Nielsen and I. L. Chuang (2000). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press.
- Zh.-Yu. Wei, D. Malz and J. I. Cirac (2023). “Efficient adiabatic preparation of tensor network states”. Physical Review Research, 5, L022037.
- A. W. Harrow, A. Hassidim and S. Lloyd (2009). “Quantum algorithm for linear systems of equations”. Physical Review Letters, 103, 150502.
- L. Zhao, Z. Zhao, P. Rebentrost and J. Fitzsimons (2021). “Compiling basic linear algebra subroutines for quantum computers”. Quantum Machine Intelligence, 3, 21.
- A. I. Zenchuk, W. Qi, A. Kumar and J. Wu (2024). “Matrix manipulations via unitary transformations and ancilla-state measurements”. Quantum Information and Computation, 24: 13–14, 1099.
- J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe and S. Lloyd (2017). “Quantum machine learning”. Nature, 549, 195.
- S. Aaronson (2015). “Read the fine print”. Nature Physics, 11, 291–293.
- P. Rebentrost, M. Mohseni and S. Lloyd (2014). “Quantum support vector machine for big data classification”. Physics Review Letters, 113, 130503.
- N. Wiebe, D. Braun and S. Lloyd (2012). “Quantum algorithm for data fitting”. Physical Review Letters, 109, 050505.
- M. Schuld, I. Sinayskiy and F. Petruccione (2016). “Prediction by linear regression on a quantum computer”. Physical Review A, 94, 022342.
- G. Wang (2017). “Quantum algorithm for linear regression”. Physical Review A, 96, 012335.
- A. Barenco, Ch. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin and H. Weinfurter (1995). “Elementary gates for quantum computation”. Physics Review A, 52, 3457.
- J. J. Vartiainen, M. Möttönen and M. M. Salomaa (2004). “Efficient decomposition of quantum gates”. Physical Review Letters, 92, 177902.
- W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling (1992). “Gray codes”, in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed., Cambridge University Press, pp. 886–888.
- X. Sun, G. Tian, S. Yang, P. Yuan and S. Zhang (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.
- G. Rosenthal (2021). “Query and depth upper bounds for quantum unitaries via Grover search”, arXiv:2111.07992 [quant-ph].
- P. Yuan and S. Zhang (2023). “Optimal qram and improved unitary synthesis by quantum circuits with any number of ancillary qubits”. Quantum, 7, 956.
- X.-M. Zhang, T. Li and X. Yuan (2022). “Quantum state preparation with optimal circuit depth: Implementations and applications”. Physical Review Letters, 129: 23, 230504.
- X.-M. Zhang, M.-H. Yung and X. Yuan (2021). “Low-depth quantum state preparation”. Physical Review Research, 3, 043200.
- P. Niemann, R. Datta and R. Wille (2016). “Logic synthesis for quantum state generation”, in 2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL). IEEE, p. 247.
- M.-X. Luo, S.-Y. Ma, Y. Deng and X. Wang (2015). “Deterministic generations of quantum state with no more than six qubits”. Quantum Information Processing, 14: 3, 901.
- S. I. Doronin, E. B. Fel’dman and A. I. Zenchuk (2020). “Solving systems of linear algebraic equations via unitary transformations on quantum processor of IBM quantum experience”. Quantum Information Processing, 19, 68.
- V. Bergholm, J. J. Vartiainen, M. Möttönen and M. M. Salomaa (2005). “Quantum circuits with uniformly controlled one-qubit gates”. Physical Review A, 71, 052330.
- I. F. Araujo, D. K. Park, F. Petruccione and A. J. da Silva1 (2021). “A divide-and-conquer algorithm for quantum state preparation”. Scientific Reports, 11: 1, 6329.
- T. H. Cormen, Ch. E. Leiserson, R. L. Rivest and C. Stein (2009). Introduction to Algorithms. MIT Press.
- M. Plesch and C. Brukner (2011). “Quantum state preparation with universal gate decompositions”. Physical Review A, 83, 032302.
- F. Mozafari, M. Soeken, H. Riener and G. De Micheli (2020). “Automatic uniform quantum state preparation using decision diagrams”, in 2020 IEEE 50th International Symposium on Multiple-Valued Logic (ISMVL), Miyazaki, Japan, pp. 170–175.
- A. Shukla and P. Vedula (2024). “An efficient quantum algorithm for preparation of uniform quantum superposition states”. Quantum Information Processing, 23, 38.
- R. I. Nepomechie and D. Raveh (2024). “Qudit Dicke state preparation”. Quantum Information & Computation, 24: 1–2, 0037.
- P. Kaye and M. Mosca (2001). “Quantum networks for generating arbitrary quantum states”, in Proceedings, International Conference on Quantum Information (ICQI). Rochester, NY, USA.
- Ar. A. Melnikov, A. A. Termanova, S. V. Dolgov, F. Neukart and M. R. Perelshtein (2023). “Quantum state preparation using tensor networks”. Quantum Science and Technology, 8, 035027.
- D. A. Puente, F. Motzoi, T. Calarco, G. Morigi and M. Rizzi (2024). “Quantum state preparation via engineered ancilla resetting”. Quantum, 8, 1299.
- K. C. Smith, E. Crane, N. Wiebe and S. M. Girvin (2023). “Deterministic constant-depth preparation of the aklt state on a quantum processor using fusion measurements”. PRX Quantum, 4, 020315.
- B. D. Clader, A. M. Dalzell, N. Stamatopoulos, G. Salton, M. Berta and W. J. Zeng (2022). “Quantum resources required to blockencode a matrix of classical data”. IEEE Transactions on Quantum Engineering, 3, 3103323.
- T. Albash and D. A. Lidar (2018). “Adiabatic quantum computation”. Reviews of Modern Physics, 90, 015002.
- V. Uotila, l. Salmenperä, L. Becker, A. M.-van de Griend, A. R. Shinde and J. K. Nurminen (2025). “Perspectives on utilization of measurements in quantum algorithms”. arXiv:2507.04325v1 [quant-ph].
- P. W. Shor (1994). “Algorithms for quantum computation: Discrete logarithms and factoring”, in Proceedings 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, pp. 124–134.
- L. Grover (1996). “A fast quantum mechanical algorithm for database search, STOC”, in 96: Proceedings 28th Annual ACM Symposium on the Theory of Computation. New York: ACM Press.
- M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio and P. J. Coles (2021). “Variational quantum algorithms”, Nature Reviews Physics, 3: 9, 625.
- S. Popescu (1994). “Bell’s inequalities versus teleportation: What is nonlocality?” Physical Review Letters, 72, 797.
- M. Horodecki, P. Horodecki and R. Horodecki (1999). “General teleportation channel, singlet fraction and quasidistillation”. Physical Review A, 60, 1888.
- L. Botelho, A. Glos, A. Kundu, J. A. Miszczak, Ö. Salehi and Z. Zimborás (2022). “Error mitigation for variational quantum algorithms through midcircuit measurements”. Physical Review A, 105: 2, 022441.
- H. Wang, L.-A. Wu, Yu. Liu and F. Nori (2010). “Measurement-based quantum phase estimation algorithm for finding eigenvalues of non-unitary matrices”. Physical Review A, 82, 062303.
- E. B. Fel’dman, J. Wu and A. I. Zenchuk (2025). “Perfect pure quantum state transfer via state restoring and ancilla measurement.” arXiv:2509.10100v2.
- T. C. Wei (2018). “Quantum spin models for measurement-based quantum computation”. Advance in Physics X, 3, 1.
- M. Zwerger, H. J. Briegel and W. Dür (2016). “Measurement-based quantum communication”. Applied Physics B, 122, 50.
- M. Zwerger, W. Dür and H. J. Briegel (2012). “Measurement-based quantum repeaters”. Physical Review A, 85, 062326.
- E. B. Fel’dman, A. I. Zenchuk, W. Qi and J. Wu (2025). “Controlled measurement, Hermitian conjugation and normalization in matrix-manipulation algorithms”. arXiv.2504.00015.
- A. Y. Kitaev, A. H. Shen and M. N. Vyalyi (2002). Classical and Quantum Computation, Graduate Studies in Mathematics, V.47, American Mathematical Society, Providence, Rhode Island.
- G. Brassard, P. Hoyer, M. Mosca and A. Tapp (2002). “Quantum amplitude amplification and estimation.” AMS Contemporary Mathematics, 305, 53.
- Ch. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. K. Wootters (1993). “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels”. Physical Review Letters, 70, 1895.
Language: English
Page range: 114 - 128
Submitted on: Oct 2, 2025
Accepted on: Jan 3, 2026
Published on: Jun 4, 2026
Published by: Cerebration Science Publishing Co., Limited
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Related subjects:
© 2026 Alexander I. Zenchuk, Wentao Qi, Junde Wu, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.