dorsal/arxiv
View SchemaEncoding a qubit in an oscillator
| Authors | Daniel Gottesman, Alexei Kitaev, John Preskill |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0008040 |
| URL | https://arxiv.org/abs/quant-ph/0008040 |
| DOI | 10.1103/PhysRevA.64.012310 |
| Journal | Phys.Rev.A64:012310,2001 |
Abstract
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.
{
"annotation_id": "fdb616eb-6624-4e9c-87d8-621c1dce50f2",
"date_created": "2026-03-02T18:01:39.265000Z",
"date_modified": "2026-03-02T18:01:39.265000Z",
"file_hash": "f7d5ac8d7a22b97ee9de6b1b521d541ee1e98220c4abefa3047c3d63fabbf923",
"private": false,
"record": {
"abstract": "Quantum error-correcting codes are constructed that embed a\nfinite-dimensional code space in the infinite-dimensional Hilbert space of a\nsystem described by continuous quantum variables. These codes exploit the\nnoncommutative geometry of phase space to protect against errors that shift the\nvalues of the canonical variables q and p. In the setting of quantum optics,\nfault-tolerant universal quantum computation can be executed on the protected\ncode subspace using linear optical operations, squeezing, homodyne detection,\nand photon counting; however, nonlinear mode coupling is required for the\npreparation of the encoded states. Finite-dimensional versions of these codes\ncan be constructed that protect encoded quantum information against shifts in\nthe amplitude or phase of a d-state system. Continuous-variable codes can be\ninvoked to establish lower bounds on the quantum capacity of Gaussian quantum\nchannels.",
"arxiv_id": "quant-ph/0008040",
"authors": [
"Daniel Gottesman",
"Alexei Kitaev",
"John Preskill"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1103/PhysRevA.64.012310",
"journal_ref": "Phys.Rev.A64:012310,2001",
"title": "Encoding a qubit in an oscillator",
"url": "https://arxiv.org/abs/quant-ph/0008040"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "e694df62-57e2-44c7-ad72-3579b57fa7d9",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}