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Trapped Ion Quantum Computing

Improved Quantum Power Method and Numerical Integration Using Quantum Singular Value Transformation

arXiv
Authors: Nhat A. Nghiem, Hiroki Sukeno, Shuyu Zhang, Tzu-Chieh Wei

Year

2024

Paper ID

65332

Status

Preprint

Abstract Read

~2 min

Abstract Words

113

Citations

N/A

Abstract

Quantum singular value transformation (QSVT) is a framework that has been shown to unify many primitives in quantum algorithms. In this work, we leverage the QSVT framework in two directions. We first show that the QSVT framework can accelerate one recently introduced quantum power method, which substantially improves its running time. Additionally, we incorporate several elementary numerical integration techniques, such as the rectangular method, Monte Carlo method, and quadrature method, into the QSVT framework, which results in polynomial speedup with respect to the size or the number of points of the grid. Our results thus provide further examples to demonstrate the potential of the QSVT and how it may enhance quantum algorithmic tasks.

Why This Paper Matters

  • This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
  • It adds a 2024 reference point for readers tracking recent quantum research.
  • Quantum singular value transformation (QSVT) is a framework that has been shown to unify many primitives in quantum algorithms.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2407.11744 [2] arXiv https://arxiv.org/abs/2407.11744 [3] Publisher https://arxiv.org/abs/2407.11744

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