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Local stabilizer codes in three dimensions without string logical operators

Jeongwan Haah · Physical Review A · 2011 · Theoretical three-dimensional stabilizer codes

Original publication

Recorded summary

Haah constructs local stabilizer codes in three dimensions without string-like logical operators. The work introduces a different geometric organisation of information and errors, associated with the fractal structure of logical operations in the cubic-code family.

Recorded limitations

This is code theory, not evidence that any fractal pattern stabilises a physical quantum computer. It does not demonstrate a Fibonacci connection or a complete self-correcting memory operating at finite temperature.

Evidence and provenance

Chapter Trust Factor uses a minimum of three distinct qualifying studies. Publication records retain their own evidence and assessment.

Study design and assessment
design
Theoretical three-dimensional stabilizer codes
assessment
category
peer-reviewed
peer Reviewed
true
basis
Theoretical three-dimensional stabilizer codes. This is not a clinical efficacy trial.
sources

https://doi.org/10.1103/PhysRevA.83.042330

reviewed At
2026-10-26
trust Factor
score
1
scope
Paper
status
assessed
randomized Controlled Trial
Not recorded
blinding
not-confirmed
peer Reviewed
true
basis
Theoretical three-dimensional stabilizer codes. This is not a clinical efficacy trial.
sources

https://doi.org/10.1103/PhysRevA.83.042330

review Scope
Existing publication-specific assessments and bibliographic indexing; no blanket full-text appraisal.
assessed At
2026-10-27
jadad
status
not-applicable
score
Not recorded
reason
Not a human randomised clinical trial.
evidence
evidence Type
Theoretical three-dimensional stabilizer codes
evidence Class
quantum_error_correction_theory
measurement
Three-dimensional local constraints and non-string logical operators.
relationship Note
Compare exact code properties and noise response before drawing connections between fractal appearance and information protection.
clinical Evidence
false
review Depth
Publisher or author abstract and bibliographic metadata; selected explanatory sections where available.
hypothesis Boundary
Connections to M9 P24, Alpha, Beta, Gamma and Epsilon remain research hypotheses. Shared geometry does not establish a shared physical mechanism.
Topics and recorded topic scores
  1. key
    general:quantum-fractal-codes
    title
    Fractal structure and information protection
    collection
    general
    trust Score
    Not recorded
Citation snapshot and identifiers
id
quantum-haah-fractal-code-2011
doi
10.1103/PhysRevA.83.042330
pmid
Not recorded
citation Snapshot
count
591
source
Crossref
retrieved At
2026-10-26
citations By Collection
general
591
Complete approved library record
id
quantum-haah-fractal-code-2011
publication Key
doi:10.1103/physreva.83.042330
aliases
None recorded
title
Local stabilizer codes in three dimensions without string logical operators
journal
Physical Review A
neurotransmitters
None recorded
year
2011
authors
Jeongwan Haah
design
Theoretical three-dimensional stabilizer codes
kind
Journal article
identity Conflict
Not recorded
doi
10.1103/PhysRevA.83.042330
pmid
Not recorded
urls

https://doi.org/10.1103/PhysRevA.83.042330

collections

general

categories

Quantum computing · Geometry and information

targets
None recorded
priority
1
quotes
None recorded
summary
Haah constructs local stabilizer codes in three dimensions without string-like logical operators. The work introduces a different geometric organisation of information and errors, associated with the fractal structure of logical operations in the cubic-code family.
limitation
This is code theory, not evidence that any fractal pattern stabilises a physical quantum computer. It does not demonstrate a Fibonacci connection or a complete self-correcting memory operating at finite temperature.
citation Count
591
citation Snapshot
count
591
source
Crossref
retrieved At
2026-10-26
study Design Assessment
category
peer-reviewed
peer Reviewed
true
basis
Theoretical three-dimensional stabilizer codes. This is not a clinical efficacy trial.
sources

https://doi.org/10.1103/PhysRevA.83.042330

reviewed At
2026-10-26
paper Trust Assessment
score
1
scope
Paper
status
assessed
randomized Controlled Trial
Not recorded
blinding
not-confirmed
peer Reviewed
true
basis
Theoretical three-dimensional stabilizer codes. This is not a clinical efficacy trial.
sources

https://doi.org/10.1103/PhysRevA.83.042330

review Scope
Existing publication-specific assessments and bibliographic indexing; no blanket full-text appraisal.
assessed At
2026-10-27
citations By Collection
general
591
topics
  1. key
    general:quantum-fractal-codes
    title
    Fractal structure and information protection
    collection
    general
    trust Score
    Not recorded
journal Key
physicalreviewa
journal Label
Physical Review A
chapter Entries
  1. id
    general-quantum-fractal-codes-quantum-haah-fractal-code-2011
    title
    Local stabilizer codes in three dimensions without string logical operators
    doi
    10.1103/PhysRevA.83.042330
    pmid
    Not recorded
    journal
    Physical Review A
    year
    2011
    published
    2011-04-22
    authors
    Jeongwan Haah
    urls

    https://doi.org/10.1103/PhysRevA.83.042330

    collections

    general

    categories

    Quantum computing · Geometry and information

    targets
    None recorded
    origin
    geometry-literature-20261026
    priority
    1
    kind
    Journal article
    design
    Theoretical three-dimensional stabilizer codes
    summary
    Haah constructs local stabilizer codes in three dimensions without string-like logical operators. The work introduces a different geometric organisation of information and errors, associated with the fractal structure of logical operations in the cubic-code family.
    finding
    Haah constructs local stabilizer codes in three dimensions without string-like logical operators. The work introduces a different geometric organisation of information and errors, associated with the fractal structure of logical operations in the cubic-code family.
    limitation
    This is code theory, not evidence that any fractal pattern stabilises a physical quantum computer. It does not demonstrate a Fibonacci connection or a complete self-correcting memory operating at finite temperature.
    citation Count
    591
    citation Snapshot
    count
    591
    source
    Crossref
    retrieved At
    2026-10-26
    study Design Assessment
    category
    peer-reviewed
    peer Reviewed
    true
    basis
    Theoretical three-dimensional stabilizer codes. This is not a clinical efficacy trial.
    sources

    https://doi.org/10.1103/PhysRevA.83.042330

    reviewed At
    2026-10-26
    evidence
    evidence Type
    Theoretical three-dimensional stabilizer codes
    evidence Class
    quantum_error_correction_theory
    measurement
    Three-dimensional local constraints and non-string logical operators.
    relationship Note
    Compare exact code properties and noise response before drawing connections between fractal appearance and information protection.
    clinical Evidence
    false
    review Depth
    Publisher or author abstract and bibliographic metadata; selected explanatory sections where available.
    hypothesis Boundary
    Connections to M9 P24, Alpha, Beta, Gamma and Epsilon remain research hypotheses. Shared geometry does not establish a shared physical mechanism.
    jadad
    status
    not-applicable
    score
    Not recorded
    reason
    Not a human randomised clinical trial.
    quotes
    None recorded
    archive Entries
    None recorded
    verified At
    2026-10-26
    source Provenance
    origin
    Verified follow-up to Gemini research notes
    notion Page
    https://app.notion.com/p/4047b9c99c5680ddb35ec2e2edf83ee4
    reviewed At
    2026-10-26
    record Id
    quantum-haah-fractal-code-2011
    source Pages
    None recorded
    paper Trust Assessment
    score
    1
    scope
    Paper
    status
    assessed
    randomized Controlled Trial
    Not recorded
    blinding
    not-confirmed
    peer Reviewed
    true
    basis
    Theoretical three-dimensional stabilizer codes. This is not a clinical efficacy trial.
    sources

    https://doi.org/10.1103/PhysRevA.83.042330

    review Scope
    Existing publication-specific assessments and bibliographic indexing; no blanket full-text appraisal.
    assessed At
    2026-10-27
    publication Key
    doi:10.1103/physreva.83.042330
    collection
    general
    chapter Number
    10
    topic Id
    quantum-fractal-codes
    topic Title
    Fractal structure and information protection
    trust Score
    Not recorded
evidence
evidence Type
Theoretical three-dimensional stabilizer codes
evidence Class
quantum_error_correction_theory
measurement
Three-dimensional local constraints and non-string logical operators.
relationship Note
Compare exact code properties and noise response before drawing connections between fractal appearance and information protection.
clinical Evidence
false
review Depth
Publisher or author abstract and bibliographic metadata; selected explanatory sections where available.
hypothesis Boundary
Connections to M9 P24, Alpha, Beta, Gamma and Epsilon remain research hypotheses. Shared geometry does not establish a shared physical mechanism.
jadad
status
not-applicable
score
Not recorded
reason
Not a human randomised clinical trial.
condition Evidence
None recorded
conditions
None recorded
topic Trust Scores
None recorded
full Text
status
curated-record
retrieval Available
false
url
https://doi.org/10.1103/PhysRevA.83.042330
checked At
2026-10-26
indexed Content
Verified metadata and original research summary are indexed. Full article text is not indexed in this update.

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