Quantum state preparation via piecewise QSVT
Efficient state preparation is essential for implementing efficient quantum algorithms. Whilst several techniques for low-cost state preparation exist, this work facilitates further classes of states, whose amplitudes are well approximated by piecewise polynomials. We show how such states can be eff...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-07-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-07-03-1786/pdf/ |
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| author | Oliver O'Brien Christoph Sünderhauf |
| author_facet | Oliver O'Brien Christoph Sünderhauf |
| author_sort | Oliver O'Brien |
| collection | DOAJ |
| description | Efficient state preparation is essential for implementing efficient quantum algorithms. Whilst several techniques for low-cost state preparation exist, this work facilitates further classes of states, whose amplitudes are well approximated by piecewise polynomials. We show how such states can be efficiently prepared using a piecewise Quantum Singular Value Transformation along with a new piecewise linear diagonal block encoding. We illustrate this with the explicit examples of $x^\alpha|x\rangle$ and $\log x|x\rangle$. Further, our technique reduces the cost of window boosted Quantum Phase Estimation by efficiently preparing the B-spline window state. We demonstrate this window state requires 50 times fewer Toffolis to prepare than the state-of-the-art Kaiser window state, and we show that the B-spline window replicates the Kaiser window's exponential reduction in tail probability for QPE. |
| format | Article |
| id | doaj-art-d34d21bcb01947469bc04e1647e87909 |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-d34d21bcb01947469bc04e1647e879092025-08-20T03:28:59ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-07-019178610.22331/q-2025-07-03-178610.22331/q-2025-07-03-1786Quantum state preparation via piecewise QSVTOliver O'BrienChristoph SünderhaufEfficient state preparation is essential for implementing efficient quantum algorithms. Whilst several techniques for low-cost state preparation exist, this work facilitates further classes of states, whose amplitudes are well approximated by piecewise polynomials. We show how such states can be efficiently prepared using a piecewise Quantum Singular Value Transformation along with a new piecewise linear diagonal block encoding. We illustrate this with the explicit examples of $x^\alpha|x\rangle$ and $\log x|x\rangle$. Further, our technique reduces the cost of window boosted Quantum Phase Estimation by efficiently preparing the B-spline window state. We demonstrate this window state requires 50 times fewer Toffolis to prepare than the state-of-the-art Kaiser window state, and we show that the B-spline window replicates the Kaiser window's exponential reduction in tail probability for QPE.https://quantum-journal.org/papers/q-2025-07-03-1786/pdf/ |
| spellingShingle | Oliver O'Brien Christoph Sünderhauf Quantum state preparation via piecewise QSVT Quantum |
| title | Quantum state preparation via piecewise QSVT |
| title_full | Quantum state preparation via piecewise QSVT |
| title_fullStr | Quantum state preparation via piecewise QSVT |
| title_full_unstemmed | Quantum state preparation via piecewise QSVT |
| title_short | Quantum state preparation via piecewise QSVT |
| title_sort | quantum state preparation via piecewise qsvt |
| url | https://quantum-journal.org/papers/q-2025-07-03-1786/pdf/ |
| work_keys_str_mv | AT oliverobrien quantumstatepreparationviapiecewiseqsvt AT christophsunderhauf quantumstatepreparationviapiecewiseqsvt |