Leírás
Abstract:
Quantum signal processing is a highly successful algorithmic primitive in
quantum computing which leads to conceptually simple and efficient quantum algorithms.
Mathematically speaking the set of implementable unitaries (i.e., quantum circuits)
are Laurent polynomials of the input unitaries. In the case of a single input matrix
the set of allowed Laurent polynomials is well understood, and has some clear characterization.
A similar characterization has been elusive in the multi-variate case even in the special
case when the input matrices (and thus the variables) are commuting. We recently refuted
a conjectured characterization, and increased our understanding of the multi-variate case,
but we are still far from a useful characterization. I will mention the most important
open questions and possible directions of generalization.
Joint work with Balázs Németh, Blanka Kövér, Boglárka Kulcsár, Roland Botond Miklósi
References:
Gilyén, A., Su, Y., Low, G. H., and Wiebe, N. Quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics.
In Proceedings of the 51st ACM Symposium on the Theory of Computing (STOC), 2019, pp. 193–204. arXiv: 1806.01838
Haah, J. Product Decomposition of Periodic Functions in Quantum Signal Processing. Quantum 3, 190 (2019). arXiv: 1806.10236
Chao, R., Ding, D., Gilyén, A., Huang, C., and Szegedy, M. Finding angles for quantum signal processing with machine precision. arXiv: 2003.02831
Chuang, I. L., and Rossi, Z. M. Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle, Quantum 6, 811 (2022). arXiv: 2205.06261
Németh, B., Kövér, B., Kulcsár, B., Miklósi, R. B., and Gilyén, A, Positive and negative results in characterizing multivariate quantum signal processing
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