Extracting GHZ states from linear cluster states
Bibliographic record
Abstract
Quantum information processing architectures typically only allow for nearest-neighbor entanglement creation. In many cases, this prevents the direct generation of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>GHZ</a:mi></a:math> states, which are commonly used for many communication and computation tasks. Here, we show how to obtain <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>GHZ</b:mi></b:math> states between nodes in a network that are connected in a straight line, naturally allowing them to initially share linear cluster states. We prove a strict upper bound of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mo>⌊</c:mo><c:mo>(</c:mo><c:mi>n</c:mi><c:mo>+</c:mo><c:mn>3</c:mn><c:mo>)</c:mo><c:mo>/</c:mo><c:mn>2</c:mn><c:mo>⌋</c:mo></c:mrow></c:math> on the size of the set of nodes sharing a <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>GHZ</d:mi></d:math> state that can be obtained from a linear cluster state of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>n</e:mi></e:math> qubits, using local Clifford unitaries, local Pauli measurements, and classical communication. Furthermore, we completely characterize all selections of nodes below this threshold that can share a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>GHZ</f:mi></f:math> state obtained within this setting. Finally, we demonstrate these transformations on the IBMQ Montreal quantum device for linear cluster states of up to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>n</g:mi><g:mo>=</g:mo><g:mn>19</g:mn></g:mrow></g:math> qubits. Published by the American Physical Society 2024
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".