Asymptotically perfect efficient quantum state transfer across uniform chains with two impurities
Bibliographic record
Abstract
The ability to transfer quantum information from one location to another with high probability is of central importance to quantum information science. Unfortunately, for the simplest system of a uniform chain (a spin chain or a particle in a one-dimensional lattice), the state transfer time grows exponentially in the chain length $N$ at fixed transfer probability. In this work we show that the addition of an impurity near each end point, coupled to the uniform chain with strength $w$, is sufficient to ensure efficient and high-probability state transfer. An eigenstate localized in the vicinity of the impurity can be tuned into resonance with chain-extended states by adjusting $w(N)\ensuremath{\propto}{N}^{1/2}$; the resulting avoided crossing yields resonant eigenstates with large amplitudes on the chain end points and approximately equidistant eigenvalues. The state transfer time scales as $t\ensuremath{\propto}{N}^{3/2}$, and its transfer probability $P$ approaches unity in the thermodynamic limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$; the error scales as $1\ensuremath{-}P\ensuremath{\propto}{N}^{\ensuremath{-}1}$. Thus, with the addition of two impurities, asymptotically perfect efficient state transfer with a uniform chain is possible even in the absence of external control.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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 teacher head, 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".