dorsal/arxiv
View SchemaEntanglement Simulations of Shor's Algorithm
| Authors | S. Parker, M. B. Plenio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0102136 |
| URL | https://arxiv.org/abs/quant-ph/0102136 |
| DOI | 10.1080/09500340110107207 |
Abstract
We demonstrate that, in the case of Shor's algorithm for factoring, highly mixed states will allow efficient quantum computation, indeed factorization can be achieved efficiently with just one initial pure qubit and a supply of initally maximally mixed qubits (S. Parker and M. B. Plenio, Phys. Rev. Lett. 85, 3049 (2000)) . This leads us to ask how this affects the entanglement in the algorithm. We thus investigate the behaviour of entanglement in Shor's algorithm for small numbers of qubits by classical computer simulation of the quantum computer at different stages of the algorithm. We find that entanglement is an intrinsic part of the algorithm and that the entanglement through the algorithm appears to be closely related to the amount of mixing. Furthermore, if the computer is in a highly mixed state any attempt to remove entanglement by further mixing of the algorithm results in a significant decrease in its efficiency.
{
"annotation_id": "806e2183-4931-402b-b6c7-52e8703a1703",
"date_created": "2026-03-02T18:01:42.486000Z",
"date_modified": "2026-03-02T18:01:42.486000Z",
"file_hash": "8a87e09ec909d5c9d7df3abe4efbc3f15f11377791cb924469fa4c64e7f408bc",
"private": false,
"record": {
"abstract": "We demonstrate that, in the case of Shor\u0027s algorithm for factoring, highly\nmixed states will allow efficient quantum computation, indeed factorization can\nbe achieved efficiently with just one initial pure qubit and a supply of\ninitally maximally mixed qubits (S. Parker and M. B. Plenio, Phys. Rev. Lett.\n85, 3049 (2000)) . This leads us to ask how this affects the entanglement in\nthe algorithm. We thus investigate the behaviour of entanglement in Shor\u0027s\nalgorithm for small numbers of qubits by classical computer simulation of the\nquantum computer at different stages of the algorithm. We find that\nentanglement is an intrinsic part of the algorithm and that the entanglement\nthrough the algorithm appears to be closely related to the amount of mixing.\nFurthermore, if the computer is in a highly mixed state any attempt to remove\nentanglement by further mixing of the algorithm results in a significant\ndecrease in its efficiency.",
"arxiv_id": "quant-ph/0102136",
"authors": [
"S. Parker",
"M. B. Plenio"
],
"categories": [
"quant-ph"
],
"doi": "10.1080/09500340110107207",
"title": "Entanglement Simulations of Shor\u0027s Algorithm",
"url": "https://arxiv.org/abs/quant-ph/0102136"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "280a6069-5107-4e2d-8dae-39e748718dc9",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}