dorsal/arxiv
View SchemaSolving Shift Problems and Hidden Coset Problem Using the Fourier Transform
| Authors | Lawrence Ip |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0205034 |
| URL | https://arxiv.org/abs/quant-ph/0205034 |
Abstract
We give a quantum algorithm for solving a shifted multiplicative character problem over Z/nZ and finite fields. We show that the algorithm can be interpreted as a matrix factorization or as solving a deconvolution problem and give sufficient conditions for a shift problem to be solved efficiently by our algorithm. We also show that combining the shift problem with the hidden subgroup problem results in a hidden coset problem. This naturally captures the redundancy in the shift due to the periodic structure of multiplicative characters over Z/nZ.
{
"annotation_id": "4d239ecc-d9de-43fb-bdb1-e110d293c1c6",
"date_created": "2026-03-02T18:01:49.221000Z",
"date_modified": "2026-03-02T18:01:49.221000Z",
"file_hash": "461b8743d0674bb51ddc56d1209d69d4e7202785e68917c5570df7c956e7122b",
"private": false,
"record": {
"abstract": "We give a quantum algorithm for solving a shifted multiplicative character\nproblem over Z/nZ and finite fields. We show that the algorithm can be\ninterpreted as a matrix factorization or as solving a deconvolution problem and\ngive sufficient conditions for a shift problem to be solved efficiently by our\nalgorithm. We also show that combining the shift problem with the hidden\nsubgroup problem results in a hidden coset problem. This naturally captures the\nredundancy in the shift due to the periodic structure of multiplicative\ncharacters over Z/nZ.",
"arxiv_id": "quant-ph/0205034",
"authors": [
"Lawrence Ip"
],
"categories": [
"quant-ph"
],
"title": "Solving Shift Problems and Hidden Coset Problem Using the Fourier Transform",
"url": "https://arxiv.org/abs/quant-ph/0205034"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "4219ea3f-1e91-4982-a52f-15ac651d3377",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}