An Efficient Quantum Algorithm for Linear System Problem in Tensor Format
<|reference_start|>An Efficient Quantum Algorithm for Linear System Problem in Tensor Format: Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of the problem dimension. However, low-complexity circuit implementations of the oracles assumed in these QLSAs constitute the major bottleneck for practical quantum speed-up in solving linear systems. In this work, we focus on the application of QLSAs for linear systems that are expressed as a low rank tensor sums, which arise in solving discretized PDEs. Previous works uses modified Krylov subspace methods to solve such linear systems with a per-iteration complexity being polylogarithmic of the dimension but with no guarantees on the total convergence cost. We propose a quantum algorithm based on the recent advances on adiabatic-inspired QLSA and perform a detailed analysis of the circuit depth of its implementation. We rigorously show that the total complexity of our implementation is polylogarithmic in the dimension, which is comparable to the per-iteration complexity of the classical heuristic methods.<|reference_end|>
@article{wu2024an,
    title={An Efficient Quantum Algorithm for Linear System Problem in Tensor
  Format},
    author={Zeguan Wu, Sidhant Misra, Tam'as Terlaky, Xiu Yang, Marc Vuffray},
    journal={arXiv preprint arXiv:2403.19829},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.19829},
    primaryClass={quant-ph cs.NA math.NA}
}