Scalable Program Implementation and Simulation of the Large-Scale Quantum Algorithm: $1024\times 1024$ Quantum Linear Solver and Beyond
| Autor: | Chen, Zhao-Yun, Xue, Cheng, Zhuang, Xi-Ning, Sun, Tai-Ping, Liu, Huan-Yu, Li, Ye, Wu, Yu-Chun, Guo, Guo-Ping |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Program implementation and simulation are essential for research in the field of quantum algorithms. However, complex and large-scale quantum algorithms can pose challenges for existing quantum programming languages and simulators. Here, we present a scalable program implementation of the quantum walk on a sparse matrix and the quantum linear solver based on the quantum walk. Our implementation is based on a practical scenario in which the sparse matrix is stored in the compressed-sparse-column format in quantum random access memory. All necessary modules are implemented unitarily and are ensured to be decomposed at the quantum gate level, including implementing a quantum binary search and a modification of the original algorithm. The program is validated using a highly efficient quantum circuit simulator which is based on the register level and sparse state representation. With only a single core, we simulate the quantum walk on a 16384-dimensional matrix with 582 qubits in 1.1 minutes per step, as well as a quantum linear solver up to 1024 dimensions and 212245 steps in 70 hours. Our work narrows the gap between the simulation of a quantum algorithm and its classical counterparts, where the asymptotic complexity of our quantum linear solver simulation approximates a classical linear solver. These program implementation and simulation techniques have the potential to expand the boundary of numerical research for large-scale quantum algorithms, with implications for the development of error-correction-era quantum computing solutions. Comment: 17 pages, 11 figures |
| Databáze: | arXiv |
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