dorsal/arxiv
View SchemaOptimum Quantum Error Recovery using Semidefinite Programming
| Authors | Andrew S. Fletcher, Peter W. Shor, Moe Z. Win |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606035 |
| URL | https://arxiv.org/abs/quant-ph/0606035 |
| DOI | 10.1103/PhysRevA.75.012338 |
Abstract
Quantum error correction (QEC) is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded in a coded subspace, and error recovery is performed via an operation designed to perfectly correct for a set of errors, presumably a large subset of the physical noise process. In this paper, we examine the choice of recovery operation. Rather than seeking perfect correction on a subset of errors, we seek a recovery operation to maximize the entanglement fidelity for a given input state and noise model. In this way, the recovery operation is optimum for the given encoding and noise process. This optimization is shown to be calculable via a semidefinite program (SDP), a well-established form of convex optimization with efficient algorithms for its solution. The error recovery operation may also be interpreted as a combining operation following a quantum spreading channel, thus providing a quantum analogy to the classical diversity combining operation.
{
"annotation_id": "76c80c6f-1516-495e-b75b-a11e8cf76aeb",
"date_created": "2026-03-02T18:02:27.358000Z",
"date_modified": "2026-03-02T18:02:27.358000Z",
"file_hash": "7ee5bdb0f285567d9a89905f843eae634ea39d67ae695f6a1475f64ba09f5dd3",
"private": false,
"record": {
"abstract": "Quantum error correction (QEC) is an essential element of physical quantum\ninformation processing systems. Most QEC efforts focus on extending classical\nerror correction schemes to the quantum regime. The input to a noisy system is\nembedded in a coded subspace, and error recovery is performed via an operation\ndesigned to perfectly correct for a set of errors, presumably a large subset of\nthe physical noise process. In this paper, we examine the choice of recovery\noperation. Rather than seeking perfect correction on a subset of errors, we\nseek a recovery operation to maximize the entanglement fidelity for a given\ninput state and noise model. In this way, the recovery operation is optimum for\nthe given encoding and noise process. This optimization is shown to be\ncalculable via a semidefinite program (SDP), a well-established form of convex\noptimization with efficient algorithms for its solution. The error recovery\noperation may also be interpreted as a combining operation following a quantum\nspreading channel, thus providing a quantum analogy to the classical diversity\ncombining operation.",
"arxiv_id": "quant-ph/0606035",
"authors": [
"Andrew S. Fletcher",
"Peter W. Shor",
"Moe Z. Win"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.012338",
"title": "Optimum Quantum Error Recovery using Semidefinite Programming",
"url": "https://arxiv.org/abs/quant-ph/0606035"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "55ea1516-becf-47b2-9a1c-fb6d96222add",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}