Estimating QSVT angles for matrix inversion with large condition numbers
Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically, with the number of angles increasing as the matrix condition nu...
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| Published in: | Journal of computational physics Vol. 525; no. C; p. 113767 |
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| Format: | Journal Article |
| Language: | English |
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15.03.2025
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| ISSN: | 0021-9991 |
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| Abstract | Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically, with the number of angles increasing as the matrix condition number grows. Computing QSVT angles for ill-conditioned problems is a numerically challenging task. We propose a numerical technique for estimating QSVT angles for large condition numbers. This technique allows one to avoid expensive numerical computations of QSVT angles and to emulate QSVT circuits for solving ill-conditioned problems. |
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| AbstractList | Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically, with the number of angles increasing as the matrix condition number grows. Computing QSVT angles for ill-conditioned problems is a numerically challenging task. We propose a numerical technique for estimating QSVT angles for large condition numbers. This technique allows one to avoid expensive numerical computations of QSVT angles and to emulate QSVT circuits for solving ill-conditioned problems. |
| ArticleNumber | 113767 |
| Author | Joseph, I. Novikau, I. |
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| Cites_doi | 10.22331/q-2023-02-02-913 10.1038/s41598-022-25727-9 10.1103/PhysRevResearch.2.043102 10.1038/s41598-023-29643-4 10.1017/S0022377824000795 10.22331/q-2024-06-13-1369 10.1103/PhysRevApplied.19.054012 10.1073/pnas.17.5.315 10.1103/PRXQuantum.2.040203 10.1103/PhysRevA.103.042419 10.1038/s41598-024-52759-0 10.1073/pnas.2026805118 10.1007/BF02546499 10.1038/s41598-023-31009-9 10.1063/5.0056974 |
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| Keywords | Quantum computing Quantum linear system algorithm Matrix inversion QSVT |
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| References | Henderson, Podzorova, Cerezo, Golden, Gleyzer, Viswanathan, O'Malley (br0110) 2023; 13 Dong, Meng, Whaley, Lin (br0040) Apr 2021; 103 Koopman (br0170) 1931; 17 (br0220) 2024 Dong, Lin, Ni, Wang (br0060) 2023 br0210 Gilyén, Su, Low, Wiebe (br0010) 2019 Ying (br0050) 2022 Krovi (br0160) 2023; 7 Akiba, Morii, Maruta (br0200) 2023; 13 Novikau, Dodin, Startsev (br0090) 2024; 90 Novikau, Dodin, Startsev (br0080) 2023; 19 Joseph (br0180) 2020; 2 Ni, Ying (br0070) 2024 Carleman (br0140) 1932; 59 Liu, Kolden, Krovi, Loureiro, Trivisa, Childs (br0150) Aug. 2021; 118 Dodin, Startsev (br0190) 2021; 28 Martyn, Rossi, Tan, Chuang (br0020) 2021; 2 Lin (br0030) 2022 Golden, O'Malley, Viswanathan (br0100) 2022; 12 Berry, Costa (br0130) 2024; 8 Henderson, Kath, Golden, Percus, O'Malley (br0120) 2024; 14 Dong (10.1016/j.jcp.2025.113767_br0040) 2021; 103 Akiba (10.1016/j.jcp.2025.113767_br0200) 2023; 13 Gilyén (10.1016/j.jcp.2025.113767_br0010) 2019 Novikau (10.1016/j.jcp.2025.113767_br0080) 2023; 19 Martyn (10.1016/j.jcp.2025.113767_br0020) 2021; 2 Lin (10.1016/j.jcp.2025.113767_br0030) Golden (10.1016/j.jcp.2025.113767_br0100) 2022; 12 Liu (10.1016/j.jcp.2025.113767_br0150) 2021; 118 Berry (10.1016/j.jcp.2025.113767_br0130) 2024; 8 Carleman (10.1016/j.jcp.2025.113767_br0140) 1932; 59 Koopman (10.1016/j.jcp.2025.113767_br0170) 1931; 17 Krovi (10.1016/j.jcp.2025.113767_br0160) 2023; 7 Novikau (10.1016/j.jcp.2025.113767_br0090) 2024; 90 Ni (10.1016/j.jcp.2025.113767_br0070) Henderson (10.1016/j.jcp.2025.113767_br0110) 2023; 13 Dodin (10.1016/j.jcp.2025.113767_br0190) 2021; 28 Ying (10.1016/j.jcp.2025.113767_br0050) Henderson (10.1016/j.jcp.2025.113767_br0120) 2024; 14 Dong (10.1016/j.jcp.2025.113767_br0060) Joseph (10.1016/j.jcp.2025.113767_br0180) 2020; 2 |
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| Snippet | Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is... |
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| StartPage | 113767 |
| SubjectTerms | Matrix inversion QSVT Quantum computing Quantum linear system algorithm |
| Title | Estimating QSVT angles for matrix inversion with large condition numbers |
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