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'''Quantum singular value transformation''' is a framework for designing [[quantum algorithm]]s. It encompasses a variety of quantum algorithms for linearproblems algebraicwhich can be solved with [[linear tasksalgebra]], including [[Hamiltonian simulation]], [[Grover's algorithm|search problems]], and [[HHL algorithm|linear system solving]].<ref name=qsvt2019>{{Cite conference |last=Gilyén |first=András |last2=Su |first2=Yuan |last3=Low |first3=Guang Hao |last4=Wiebe |first4=Nathan |date=June 2019 |title=Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics |conference=STOC 2019 |url=https://dl.acm.org/doi/10.1145/3313276.3316366 |language=en |publisher=ACM |pages=193–204 |doi=10.1145/3313276.3316366 |isbn=978-1-4503-6705-9}}</ref><ref name=grand_unification2021>{{Cite journal |arxiv = 2105.02859 |last1 = Martyn|first1 = John M. |last2= Rossi |first2 = Zane M |last3=Tan |first3=Andrew K. |last4=Chuang |first4=Isaac L. |title = Grand Unification of Quantum Algorithms|journal = PRX Quantum|volume = 2|pages = 040203|year = 2021| issue=4 |publisher=American Physical Society|doi =10.1103/PRXQuantum.2.040203| bibcode=2021PRXQ....2d0203M |url=https://link.aps.org/doi/10.1103/PRXQuantum.2.040203}}</ref><ref>{{Cite journal |last=Arrazola |first=Juan Miguel |date=2023-05-23 |title=Intro to QSVT |url=https://pennylane.aiundefined/ |journal=PennyLane Demos |language=en}}</ref> It was introduced in 2018 by András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe, generalizing algorithms for Hamiltonian simulation of Guang Hao Low and [[Isaac Chuang]] inspired by signal processing.<ref name=LC2016>{{Cite journal |arxiv = 1606.02685 |last1 = Low|first1 = Guang Hao |last2= Chuang |first2 = Isaac |title = Optimal Hamiltonian Simulation by Quantum Signal Processing|journal = Physical Review Letters|volume = 118|pages = 010501|year = 2017| issue=1 |bibcode = 2017PhRvL.118a0501L|doi = 10.1103/PhysRevLett.118.010501|pmid = 28106413| s2cid=1118993 }}</ref>
==High-level description==
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