dorsal/arxiv
View SchemaThe Heisenberg Representation of Quantum Computers
| Authors | Daniel Gottesman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9807006 |
| URL | https://arxiv.org/abs/quant-ph/9807006 |
| Journal | Group22: Proceedings of the XXII International Colloquium on Group Theoretical Methods in Physics, eds. S. P. Corney, R. Delbourgo, and P. D. Jarvis, pp. 32-43 (Cambridge, MA, International Press, 1999) |
Abstract
Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of describing them on classical computers - also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.
{
"annotation_id": "d8189e46-60fb-4589-ab47-5023501eff76",
"date_created": "2026-03-02T18:02:44.591000Z",
"date_modified": "2026-03-02T18:02:44.591000Z",
"file_hash": "c592a131525181f66bc9b8685c428f2c4d083c16b72da222f0985ef834d9c141",
"private": false,
"record": {
"abstract": "Since Shor\u0027s discovery of an algorithm to factor numbers on a quantum\ncomputer in polynomial time, quantum computation has become a subject of\nimmense interest. Unfortunately, one of the key features of quantum computers -\nthe difficulty of describing them on classical computers - also makes it\ndifficult to describe and understand precisely what can be done with them. A\nformalism describing the evolution of operators rather than states has proven\nextremely fruitful in understanding an important class of quantum operations.\nStates used in error correction and certain communication protocols can be\ndescribed by their stabilizer, a group of tensor products of Pauli matrices.\nEven this simple group structure is sufficient to allow a rich range of quantum\neffects, although it falls short of the full power of quantum computation.",
"arxiv_id": "quant-ph/9807006",
"authors": [
"Daniel Gottesman"
],
"categories": [
"quant-ph"
],
"journal_ref": "Group22: Proceedings of the XXII International Colloquium on Group\n Theoretical Methods in Physics, eds. S. P. Corney, R. Delbourgo, and P. D.\n Jarvis, pp. 32-43 (Cambridge, MA, International Press, 1999)",
"title": "The Heisenberg Representation of Quantum Computers",
"url": "https://arxiv.org/abs/quant-ph/9807006"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a84aad81-cdc3-4fa6-b805-0a2b5f90449e",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}