We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.
 S. Bravyi and D. Gosset, Phys. Rev. Lett. 116, 250501 (2016).
 D. J. Bernstein, ``Introduction to post-quantum cryptography,'' in Post-Quantum Cryptography, edited by D. J. Bernstein, J. Buchmann, and E. Dahmen (Springer Berlin Heidelberg, Berlin, Heidelberg, 2009) pp. 1–14.
 E. Lucero, R. Barends, Y. Chen, J. Kelly, M. Mariantoni, A. Megrant, P. O'Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, Y. Yin, A. N. Cleland, and J. M. Martinis, Nat. Phys. 8, 719 (2012).
 E. Anderson, Z. Bai, C. Bischof, L. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users' Guide, Third ed. (Society for Industrial and Applied Mathematics, Philadelphia, 1999).
 R. L. Graham, T. S. Woodall, and J. M. Squyres, in Parallel Processing and Applied Mathematics: 6th International Conference, PPAM 2005, Poznań, Poland, September 11-14, 2005, Revised Selected Papers, edited by R. Wyrzykowski, J. Dongarra, N. Meyer, and J. Waśniewski (Springer Berlin Heidelberg, Berlin, Heidelberg, 2006) pp. 228–239.
 Q. Wang, X. Zhang, Y. Zhang, and Q. Yi, in SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (ACM, New York, 2013) pp. 25:1–25:12.
 Thien Nguyen, Dmitry Lyakh, Eugene Dumitrescu, David Clark, Jeff Larkin, and Alexander McCaskey, "Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale", ACM Transactions on Quantum Computing 4 1, 1 (2023).
 Honghui Shang, Li Shen, Yi Fan, Zhiqian Xu, Chu Guo, Jie Liu, Wenhao Zhou, Huan Ma, Rongfen Lin, Yuling Yang, Fang Li, Zhuoya Wang, Yunquan Zhang, and Zhenyu Li, SC22: International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2022) ISBN:978-1-6654-5444-5.
 Kouichi Okunishi, Tomotoshi Nishino, and Hiroshi Ueda, "Developments in the Tensor Network — from Statistical Mechanics to Quantum Entanglement", Journal of the Physical Society of Japan 91 6, 062001 (2022).
 Maxime Dupont, Nicolas Didier, Mark J. Hodson, Joel E. Moore, and Matthew J. Reagor, "Calibrating the Classical Hardness of the Quantum Approximate Optimization Algorithm", PRX Quantum 3 4, 040339 (2022).
 Andrés Gómez, Álvaro Leitao, Alberto Manzano, Daniele Musso, María R. Nogueiras, Gustavo Ordóñez, and Carlos Vázquez, "A Survey on Quantum Computational Finance for Derivatives Pricing and VaR", Archives of Computational Methods in Engineering 29 6, 4137 (2022).
 Jakob Unfried, Johannes Hauschild, and Frank Pollmann, "Fast time evolution of matrix product states using the QR decomposition", Physical Review B 107 15, 155133 (2023).
 Shi-Ju Ran, "Encoding of matrix product states into quantum circuits of one- and two-qubit gates", Physical Review A 101 3, 032310 (2020).
 Samuel Jaques and Thomas Häner, "Leveraging State Sparsity for More Efficient Quantum Simulations", ACM Transactions on Quantum Computing 3 3, 1 (2022).
 Gilberto J. Díaz T, Carlos J. Barrios H., Luiz A. Steffenel, and Jean F. Couturier, Communications in Computer and Information Science 1660, 205 (2022) ISBN:978-3-031-23820-8.
 Yi-Ting Chen, Collin Farquhar, and Robert M. Parrish, "Low-rank density-matrix evolution for noisy quantum circuits", npj Quantum Information 7 1, 61 (2021).
 Manas Sajjan, Junxu Li, Raja Selvarajan, Shree Hari Sureshbabu, Sumit Suresh Kale, Rishabh Gupta, Vinit Singh, and Sabre Kais, "Quantum machine learning for chemistry and physics", Chemical Society Reviews 51 15, 6475 (2022).
 He-Liang Huang, Xiao-Yue Xu, Chu Guo, Guojing Tian, Shi-Jie Wei, Xiaoming Sun, Wan-Su Bao, and Gui-Lu Long, "Near-term quantum computing techniques: Variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation", Science China Physics, Mechanics & Astronomy 66 5, 250302 (2023).
 Maxime Dupont, Nicolas Didier, Mark J. Hodson, Joel E. Moore, and Matthew J. Reagor, "Entanglement perspective on the quantum approximate optimization algorithm", Physical Review A 106 2, 022423 (2022).
 Holm Gero Hümmler, Relativer Quantenquark 105 (2019) ISBN:978-3-662-58419-4.
 Alexander McCaskey, Eugene Dumitrescu, Mengsu Chen, Dmitry Lyakh, and Travis Humble, "Validating quantum-classical programming models with tensor network simulations", PLoS ONE 13 12, e0206704 (2018).
 Baonan Wang, Xiaoting Yang, and Dan Zhang, "Research on Quantum Annealing Integer Factorization Based on Different Columns", Frontiers in Physics 10, 914578 (2022).
 Baonan Wang, Feng Hu, Haonan Yao, and Chao Wang, "Prime factorization algorithm based on parameter optimization of Ising model", Scientific Reports 10, 7106 (2020).
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