Optimising Matrix Product State Simulations of Shor’s Algorithm

Aidan Dang, Charles D. Hill, and Lloyd C. L. Hollenberg

Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Parkville, Victoria 3010, Australia

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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.

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[5] 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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