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Quantum State Preparation Representation

On equivalent methods for functional determinants

arXiv
Authors: Matthias Carosi

Year

2026

Paper ID

3886

Status

Preprint

Abstract Read

~2 min

Abstract Words

105

Citations

0

Abstract

Computing functional determinants of differential operators is central to any field-theoretical calculation relying on a saddle-point expansion. A variety of approaches is available for the computation that avoid having to know the eigenspectrum of the operator, and in particular the Gel'fand-Yaglom theorem and the Green's function method. In this note, we show how both approaches can be constructed using a contour integral argument and conclude that these are completely equivalent for computing ratios of determinants of one-dimensional operators. Furthermore, we comment on the presence of vanishing as well as negative eigenvalues and show how the Green's function method provides a natural prescription for handling them.

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  • This paper contributes to the Quantum State Preparation & Representation research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • Computing functional determinants of differential operators is central to any field-theoretical calculation relying on a saddle-point expansion.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.08686 [2] arXiv https://arxiv.org/abs/2601.08686 [3] Publisher https://arxiv.org/abs/2601.08686

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Current Paper #3886 #68971 On solutions of the Schrödinger...

External citation index: OpenAlex citation signal • updated 2026-06-14 12:34:26

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