Acknowledgements, Declarations, Data Availability Statement, and References

Authors: (1) Nhat A. Nghiem, Department of Physics and Astronomy, State University of New York (email: nhatanh.nghiemvu@stonybrook.edu); (2) Tzu-Chieh Wei, Department of Physics and Astronomy, State University of New York and C. N. Yang Institute for Theoretical Physics, State University of New York. Table of Links Main Procedure Applications Discussion and Conclusion Acknowledgements, Declarations, Data Availability Statement, and References Appendix ACKNOWLEDGEMENTS This work was supported in part by the U. S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under contract number DE-SC0012704. We also acknowledge the support from a Seed Grant from Stony Brook University’s Office of the Vice President for Research. DECLARATIONS On behalf of all authors, the corresponding author states that there is no conflict of interest. DATA AVAILABILITY STATEMENT There is no data generated in this work. References [1] Aram W Harrow, Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for linear systems of equations. Physical review letters, 103(15):150502, 2009. [2] Andrew M Childs, Robin Kothari, and Rolando D Somma. Quantum algorithm for systems of linear equations with exponentially improved dependence on precision. SIAM Journal on Computing, 46(6):1920–1950, 2017. [3] B David Clader, Bryan C Jacobs, and Chad R Sprouse. Preconditioned quantum linear system algorithm. Physical review letters, 110(25):250504, 2013. [4] Nathan Wiebe, Daniel Braun, and Seth Lloyd. Quantum algorithm for data fitting. Physical review letters, 109(5):050505, 2012. [5] Nhat A Nghiem and Tzu-Chieh Wei. Quantum algorithm for estimating eigenvalue. arXiv preprint arXiv:2211.06179, 2022. [6] Dominic W Berry, Andrew M Childs, and Robin Kothari. Hamiltonian simulation with nearly optimal dependence on all parameters. In 2015 IEEE 56th annual symposium on foundations of computer science, pages 792–809. IEEE, 2015. [7] Dominic W Berry, Graeme Ahokas, Richard Cleve, and Barry C Sanders. Efficient quantum algorithms for simulating sparse hamiltonians. Communications in Mathematical Physics, 270(2):359–371, 2007. [8] Dominic W Berry and Andrew M Childs. Black-box hamiltonian simulation and unitary implementation. Quantum Information and Computation, 12:29–62, 2009. [9] Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp. Quantum amplitude amplification and estimation. Contemporary Mathematics, 305:53–74, 2002. [10] Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd. Quantum support vector machine for big data classification. Physical review letters, 113(13):130503, 2014. [11] E. Knill and R. Laflamme. Power of one bit of quantum information. Phys. Rev. Lett., 81:5672–5675, Dec 1998. [12] Peter W. Shor and Stephen P. Jordan. Estimating jones polynomials is a complete problem for one clean qubit. 8(8):681–714, 2008. [13] Michael A Nielsen and Isaac Chuang. Quantum computation and quantum information, 2002. This paper is available on arxiv under CC 4.0 license. Authors: (1) Nhat A. Nghiem, Department of Physics and Astronomy, State University of New York (email: nhatanh.nghiemvu@stonybrook.edu); (2) Tzu-Chieh Wei, Department of Physics and Astronomy, State University of New York and C. N. Yang Institute for Theoretical Physics, State University of New York. Authors: Authors: (1) Nhat A. Nghiem, Department of Physics and Astronomy, State University of New York (email: nhatanh.nghiemvu@stonybrook.edu); (2) Tzu-Chieh Wei, Department of Physics and Astronomy, State University of New York and C. N. Yang Institute for Theoretical Physics, State University of New York. Table of Links Main Procedure Main Procedure Applications Applications Discussion and Conclusion Discussion and Conclusion Acknowledgements, Declarations, Data Availability Statement, and References Acknowledgements, Declarations, Data Availability Statement, and References Appendix Appendix ACKNOWLEDGEMENTS This work was supported in part by the U. S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under contract number DE-SC0012704. We also acknowledge the support from a Seed Grant from Stony Brook University’s Office of the Vice President for Research. DECLARATIONS On behalf of all authors, the corresponding author states that there is no conflict of interest. DATA AVAILABILITY STATEMENT There is no data generated in this work. References [1] Aram W Harrow, Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for linear systems of equations. Physical review letters, 103(15):150502, 2009. [2] Andrew M Childs, Robin Kothari, and Rolando D Somma. Quantum algorithm for systems of linear equations with exponentially improved dependence on precision. SIAM Journal on Computing, 46(6):1920–1950, 2017. [3] B David Clader, Bryan C Jacobs, and Chad R Sprouse. Preconditioned quantum linear system algorithm. Physical review letters, 110(25):250504, 2013. [4] Nathan Wiebe, Daniel Braun, and Seth Lloyd. Quantum algorithm for data fitting. Physical review letters, 109(5):050505, 2012. [5] Nhat A Nghiem and Tzu-Chieh Wei. Quantum algorithm for estimating eigenvalue. arXiv preprint arXiv:2211.06179, 2022. [6] Dominic W Berry, Andrew M Childs, and Robin Kothari. Hamiltonian simulation with nearly optimal dependence on all parameters. In 2015 IEEE 56th annual symposium on foundations of computer science, pages 792–809. IEEE, 2015. [7] Dominic W Berry, Graeme Ahokas, Richard Cleve, and Barry C Sanders. Efficient quantum algorithms for simulating sparse hamiltonians. Communications in Mathematical Physics, 270(2):359–371, 2007. [8] Dominic W Berry and Andrew M Childs. Black-box hamiltonian simulation and unitary implementation. Quantum Information and Computation, 12:29–62, 2009. [9] Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp. Quantum amplitude amplification and estimation. Contemporary Mathematics, 305:53–74, 2002. [10] Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd. Quantum support vector machine for big data classification. Physical review letters, 113(13):130503, 2014. [11] E. Knill and R. Laflamme. Power of one bit of quantum information. Phys. Rev. Lett., 81:5672–5675, Dec 1998. [12] Peter W. Shor and Stephen P. Jordan. Estimating jones polynomials is a complete problem for one clean qubit. 8(8):681–714, 2008. [13] Michael A Nielsen and Isaac Chuang. Quantum computation and quantum information, 2002. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv