References
- Benioff P (1980). The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines. J. Stat. Phys., 22(5): 563591.
- Manin Y I (1980). Computable and noncomputable (in Russian). Sov. Radio, 13–15.
- Deutsch D (1985). Quantum theory, the Church -Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A, 400(1818): 97117.
- Shor P W (1994). Algorithms for quantum computation: discrete logarithms and factoring. Proceedings 35th Annual Symposium on Foundations of Computer Science. IEEE: 124134.
- Shor P W (1999). Polynomial time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev., 41(2): 303332.
- Grover L K (1996). A fast quantum mechanical algorithm for database search. Proceedings of the 28th Annual ACM Symposium on Theory of Computing. 212219.
- Harrow A W, Hassidim A and Lloyd S (2009). Quantum algorithm for linear systems of equations. Phys. Rev. Lett., 103(15): 150502.
- Clader B D, Jacobs B C and Sprouse C R (2013). Preconditioned quantum linear system algorithm. Phys. Rev. Lett., 110(25): 250504.
- Coppersmith D and Winograd S (1990). Matrix multiplication via arithmetic progressions. J. Symb. Comput., 9(3): 251–280.
- Weinstein Y S, Pravia M A, Fortunato E M, et al. (2001). Implementation of the quantum Fourier transform. Phys. Rev. Lett., 86(9): 1889.
- Nielsen M A, Chuang I (2000). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press.
- Wang H, Wu L, Liu Y, et al. (2010). Measurement based quantum phase estimation algorithm for finding eigenvalues of nonunitary matrices. Phys. Rev. A, 82(6):062303.
- Motta M, Ye E, McClean J R, et al. (2021). Low rank representations for quantum simulation of electronic structure. Npj Quantum Inf., 7: 83.
- Kockum A F, Soro A and García-Álvarez L, et al. Lecture Notes on Quantum Computing. arXiv: 2311.08445 [quant-ph].
- Prakash A (2014). Quantum algorithms for linear algebra and machine learning. Ph.D. Thesis, UC Berkeley.
- Trotter H F (1959). On the product of semi-groups of operators. P. Am. Math. Soc., 10(4): 545-551.
- Zhao Z, Fitzsimons J K and Fitzsimons J F (2019). Quantumassisted Gaussian process regression. Phys. Rev. A, 99(5): 052331.
- Stolze J, Zenchuk A I (2019). Computing scalar products via a twoterminal quantum transmission line. Phys. Lett. A, 383(34): 125978.
- Wentao Q, Alexander I Z, Asutosh K and Junde W (2024). Quantum algorithms for matrix operations and linear systems of equations. Commun. Theor. Phys., 76: 035103.
- Alexander I Z, Wentao Q, Asutosh K and Junde W (2004). Matrix manipulations via unitary transformations and ancilla state measurements. Quantum Inf. Comput., 24(13): 1099-1109.
- Alexander I Z, Georgii A B, Wentao Q, Asutosh K and Junde W (2025). Quantum Algorithms for Calculating Determinant and Inverse of Matrix and Solving Linear Algebraic Systems. Quantum Inf. Comput., 25(2): 195-215.
- Alexander I Z, Wentao Q and Junde W (2025). Matrix encoding method in variational quantum singular value decomposition. Quantum Inf. Comput., 25(4): 356-368.
- Edward B F, Alexander I Z, Wentao Q and Junde W, Controlled measurement, Hermitian conjugation and normalization in matrix-manipulation algorithms. arXiv:2504.00015 [quant-ph].
- Kitaev A Y, Shen A H and Vyalyi M N (2002). Classical and Quantum Computation, Graduate Studies in Mathematics, V.47, American Mathematical Society, Providence, Rhode Island.