Periodicity of bipartite walk on biregular graphs with conditional spectra
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Bibliographic record
Abstract
Abstract In this paper we study a class of discrete quantum walks, known as bipartite walks. These include the well-known Grover’s walks. A discrete quantum walk is given by the powers of a unitary matrix U indexed by arcs or edges of the underlying graph. The walk is periodic if U k = I for some positive integer k . Kubota has given a characterization of periodicity of Grover’s walk when the walk is defined on a regular bipartite graph with at most five eigenvalues. We extend Kubota’s results—if a biregular graph G has eigenvalues whose squares are algebraic integers with degree at most two, we characterize periodicity of the bipartite walk over G in terms of its spectrum. We apply periodicity results of bipartite walks to get a characterization of periodicity of Grover’s walk on regular graphs.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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