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arXiv · 2303.06890

Scalable Program Implementation and Simulation of the Large-Scale Quantum Algorithm: $1024\times 1024$ Quantum Linear Solver and Beyond

Zhao-Yun Chen·Cheng Xue·Xi-Ning Zhuang·Tai-Ping Sun·Huan-Yu Liu·Ye Li·Yu-Chun Wu·Guo-Ping Guo
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Abstract

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.

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Zhao-Yun Chen, Cheng Xue, Xi-Ning Zhuang, Tai-Ping Sun, Huan-Yu Liu, Ye Li, Yu-Chun Wu, Guo-Ping Guo. 2023-03-13. Scalable Program Implementation and Simulation of the Large-Scale Quantum Algorithm: $1024\times 1024$ Quantum Linear Solver and Beyond. https://arxiv.org/abs/2303.06890

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