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Perfect Quantum Error Correction Code

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, Wojciech Hubert Zurek

Quantum Physics · Submitted 27 Feb 1996

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment.

how it is stated · asserted 0.97 read the record →

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arXiv IDquant-ph/9602019 (version 1)
Pith IDDPWQEKNT, Pith's permanent record of this paper and its review
CitationCesar Miquel, Juan Pablo Paz, Raymond Laflamme, Wojciech Hubert Zurek. "Perfect Quantum Error Correction Code." arXiv:quant-ph/9602019 (1996). https://pith.science/paper/DPWQEKNT
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,817 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.91 · compares with prior results 0.10 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We give a simple circuit which takes the initial state with four extra qubits in the state |0> to the encoded state. The circuit can be converted into a decoding one by simply running it backward. Reading the extra four qubits at the decoder's output we learn which one of the sixteen alternatives (no error plus all fifteen possible 1-bit errors) was realized. The original state of the encoded qubit can then be restored by a simple unitary transformation.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. contribution 1.00 0.91 0.70 asserted 0.97
s1 To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. method 0.75 0.85 0.28 asserted 1.00
s2 We give a simple circuit which takes the initial state with four extra qubits in the state |0> to the encoded state. method 0.88 0.93 0.06 asserted 1.00
s3 The circuit can be converted into a decoding one by simply running it backward. method 0.94 0.79 0.05 asserted 0.90
s4 Reading the extra four qubits at the decoder's output we learn which one of the sixteen alternatives (no error plus all fifteen possible 1-bit errors) was realized. method 0.94 0.85 0.10 asserted 0.99
s5 The original state of the encoded qubit can then be restored by a simple unitary transformation. method 0.92 0.79 0.22 asserted 0.97

What kind of paper the classifier reports this is: method or tool 0.91 · evidence from proof or derivation 0.90.

What was examined, and what was not

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  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We give a simple circuit which takes the initial state with four extra qubits in the state |0> to the encoded state. The circuit can be converted into a decoding one by simply running it backward. Reading the extra four qubits at the decoder's output we learn which one of the sixteen alternatives (no error plus all fifteen possible 1-bit errors) was realized. The original state of the encoded qubit can then be restored by a simple unitary transformation.

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References
How the literature uses it

24 arXiv papers cite this in 35 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 26 sentences without a confident label

Compares with it 2 papers
Cites it as background 6 papers

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