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Trapped Ion Quantum Computing Quantum Machine Learning Quantum Chemistry

Fast Laplace transforms on quantum computers

arXiv
Authors: Julien Zylberman

Year

2024

Paper ID

6282

Status

Preprint

Abstract Read

~2 min

Abstract Words

125

Citations

N/A

Abstract

While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT), which enables the implementation of Ntimes N discrete Laplace transforms on quantum states encoded in lceil log2(N)rceil-qubits. In many cases, the associated quantum circuits have a depth that scales with N as O\(log(log(N\))) and a size that scales as O\(log(N\)), requiring exponentially fewer operations and double-exponentially less computational time than their classical counterparts. These efficient scalings open the possibility of developing a new class of quantum algorithms based on Laplace transforms, with potential applications in physics, engineering, chemistry, machine learning, and finance.

Why This Paper Matters

  • This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
  • It adds a 2024 reference point for readers tracking recent quantum research.
  • While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2412.05173 [2] arXiv https://arxiv.org/abs/2412.05173 [3] Publisher https://arxiv.org/abs/2412.05173

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