RECORD
Quantum Walk on the Line through Potential Barriers
Quantum Physics · Submitted 23 Sep 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Rather, the $\Theta(t)$ dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments.
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.
Open the compiled record
The abstract, sentence by sentence
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the particle may need to tunnel through a potential barrier to hop, and a naive calculation suggests this could eliminate the ballistic transport. We show by explicit calculation, however, that such a loss does not occur. Rather, the $\Theta(t)$ dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s1 | In physical implementations of the walk, however, the particle may need to tunnel through a potential barrier to hop, and a naive calculation suggests this could eliminate the ballistic transport. | background 0.83 | 0.07 | 0.03 | hedged possibility 1.00 |
| s2 | We show by explicit calculation, however, that such a loss does not occur. | result 0.83 | 0.94 | 0.46 | asserted 1.00 |
| s3 | Rather, the $\Theta(t)$ dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments. | result 0.87 | 0.93 | 0.87 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the particle may need to tunnel through a potential barrier to hop, and a naive calculation suggests this could eliminate the ballistic transport. We show by explicit calculation, however, that such a loss does not occur. Rather, the $\Theta(t)$ dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments.
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 3 sentences without a confident label
Uses the method or tool of 1 paper
-
As described in [ref] , this can be done using the method of steepest descent, where we examine the time-oscillatory portion of [ref] and [ref], which is [equation] where we have defined [equation] From the analysis of [ref] , the part we care about is the movement of the peak in probability (e.g., the leading right peak in Figure [ref]).
Quantum Walk on the Line · Analysis with Potential Barriers · 1.00
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.