# Quantum Algorithm, Gaussian Sums, and Topological Invariants

Source: [Quantum Algorithm, Gaussian Sums, and Topological Invariants](<https://www.sota2.com/research/paper/68fa23782c2a376019398205>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:31.737Z

Authors: K. Shiokawa

Published: 2009-03-10T05:48:38.000Z

## Abstract

Certain quantum topological invariants of three manifolds can be written in the form of the Gaussian sum. It is shown that such topological invariants can be approximated efficiently by a quantum computer. The invariants discussed here are obtained as a partition function of the gauge theory on three manifolds with various gauge groups. Our algorithms are applicable to Abelian and finite gauge groups and to some classes of non-Abelian gauge groups. These invariants can be directly estimated by the nuclear magnetic resonance (NMR) technique used for evaluating the Gaussian sum.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0903.1688>)

[PDF](<https://arxiv.org/pdf/0903.1688.pdf>)