Comment on "Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle"

Hitomi Mori; Kaoru Mizuta; Keisuke Fujii

doi:10.22331/q-2024-10-29-1512

Comment on “Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle”

Hitomi Mori¹, Kaoru Mizuta^2,3, and Keisuke Fujii^1,4,3,5

¹Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
²Department of Applied Physics, The University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-8656, Japan
³Center for Quantum Computing, RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198, Japan
⁴Center for Quantum Information and Quantum Biology, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
⁵Fujitsu Quantum Computing Joint Research Division at QIQB, Osaka University, 1-2 Machikaneyama, Toyonaka 560-0043, Japan

Published:	2024-10-29, volume 8, page 1512
Eprint:	arXiv:2310.00918v2
Doi:	https://doi.org/10.22331/q-2024-10-29-1512
Citation:	Quantum 8, 1512 (2024).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Multivariable Quantum Signal Processing (M-QSP) [1] is expected to provide an efficient means to handle polynomial transformations of multiple variables simultaneously. However, we identified several inconsistencies in the main theorem, where necessary and sufficient conditions for achievable polynomials are provided, and its proof in Ref. [1]. Moreover, a counterexample to the conjecture in Ref. [1], based on which the main theorem is constructed, is presented in Ref. [2], meaning the requirement of the conjecture should be included as a condition in the theorem. Here we note our observations and propose the revised necessary conditions for M-QSP. We also show that these necessary conditions cannot be sufficient conditions, and thus some additional condition on top of these revisions is essentially required for the complete M-QSP theorem.

► BibTeX data

@article{Mori2024comment,
  doi = {10.22331/q-2024-10-29-1512},
  url = {https://doi.org/10.22331/q-2024-10-29-1512},
  title = {Comment on "{M}ultivariable quantum signal processing ({M}-{QSP}): prophecies of the two-headed oracle"},
  author = {Mori, Hitomi and Mizuta, Kaoru and Fujii, Keisuke},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1512},
  month = oct,
  year = {2024}
}

► References

[1] Zane M. Rossi and Isaac L. Chuang. ``Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle''. Quantum 6, 811 (2022).
https://doi.org/10.22331/q-2022-09-20-811

[2] Balázs Németh, Blanka Kövér, Boglárka Kulcsár, Roland Botond Miklósi, and András Gilyén. ``On variants of multivariate quantum signal processing and their characterizations'' (2023). arXiv:2312.09072.
arXiv:2312.09072

[3] Peter W. Shor. ``Algorithms for quantum computation: discrete logarithms and factoring''. Proceedings 35th Annual Symposium on Foundations of Computer Science, 124-134 (1994).
https://doi.org/10.1109/SFCS.1994.365700

[4] Seth Lloyd. ``Universal quantum simulators''. Science 273, 1073–1078 (1996).
https://doi.org/10.1126/science.273.5278.1073

[5] Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd. ``Quantum algorithm for linear systems of equations''. Phys. Rev. Lett. 103, 150502 (2009).
https://doi.org/10.1103/PhysRevLett.103.150502

[6] Guang H. Low, Theodore J. Yoder, and Isaac L. Chuang. ``Methodology of resonant equiangular composite quantum gates''. Phys. Rev. X 6, 041067 (2016).
https://doi.org/10.1103/PhysRevX.6.041067

[7] András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe. ``Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics''. Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, 193^^e2^^80^^93204 (2019).
https://doi.org/10.1145/3313276.3316366

[8] Lorenzo Laneve and Stefan Wolf. ``On multivariate polynomials achievable with quantum signal processing'' (2024). arXiv:2407.20823.
arXiv:2407.20823

[9] Niladri Gomes, Hokiat Lim, and Nathan Wiebe. ``Multivariable qsp and bosonic quantum simulation using iterated quantum signal processing'' (2024). arXiv:2408.03254.
arXiv:2408.03254

[10] Hitomi Mori, Kosuke Mitarai, and Keisuke Fujii. ``Efficient state preparation for multivariate monte carlo simulation'' (2024). arXiv:2409.07336.
arXiv:2409.07336

[11] Yuki Ito, Hitomi Mori, Kazuki Sakamoto, and Keisuke Fujii. ``Polynomial time constructive decision algorithm for multivariable quantum signal processing'' (2024). arXiv:2410.02332.
arXiv:2410.02332

Cited by

[1] Lorenzo Laneve, "An adversary bound for quantum signal processing", Quantum 10, 2025 (2026).

[2] Yuki Ito, Hitomi Mori, Kazuki Sakamoto, and Keisuke Fujii, "Polynomial time constructive decision algorithm for multivariable quantum signal processing", Quantum 10, 2102 (2026).

[3] Lorenzo Laneve and Stefan Wolf, "On multivariate polynomials achievable with quantum signal processing", Quantum 9, 1641 (2025).

[4] Matthias Rosenkranz, Eric Brunner, Gabriel Marin-Sanchez, Nathan Fitzpatrick, Silas Dilkes, Yao Tang, Yuta Kikuchi, and Marcello Benedetti, "Quantum state preparation for multivariate functions", Quantum 9, 1703 (2025).

[5] Christopher F. Kane, Siddharth Hariprakash, Neel S. Modi, Michael Kreshchuk, and Christian W Bauer, "Block encoding bosons by signal processing", Quantum 9, 1747 (2025).

[6] Jungsoo Hong, Seong Ho Kim, Seung Kyu Min, and Joonsuk Huh, "Oscillator–qubit generalized quantum signal processing: a case study of the uracil cation vibronic model", Chemical Science 17 24, 11911 (2026).

[7] Yuki Ito, Hitomi Mori, Kazuki Sakamoto, and Keisuke Fujii, "Polynomial time constructive decision algorithm for multivariable quantum signal processing", arXiv:2410.02332, (2024).

[8] Zane M. Rossi, "A Solovay-Kitaev theorem for quantum signal processing", arXiv:2505.05468, (2025).

[9] S. E. Skelton, "The Hitchhiker's Guide to QSP pre-processing", arXiv:2501.05977, (2025).

The above citations are from Crossref's cited-by service (last updated successfully 2026-07-15 08:54:08) and SAO/NASA ADS (last updated successfully 2026-07-14 17:02:42). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch ADS cited-by data during last attempt 2026-07-15 08:54:08: Cannot retrieve data from ADS due to rate limitations.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.