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Simple Quantum Coins Enable Pretty Good State Transfer on Every Hypercube

Combinatorics 2024-12-31 v1 Discrete Mathematics Quantum Physics

Abstract

We consider pretty good state transfer in coined quantum walks between antipodal vertices on the hypercube QdQ_d. When dd is a prime, this was proven to occur in the arc-reversal walk with Grover coins. We extend this result by constructing weighted Grover coins that enable pretty good state transfer on every QdQ_d. Our coins are real, and require modification of the weight on only one arc per vertex. We also generalize our approach and establish a sufficient condition for pretty good state transfer to occur on other graphs.

Cite

@article{arxiv.2412.20753,
  title  = {Simple Quantum Coins Enable Pretty Good State Transfer on Every Hypercube},
  author = {Hanmeng Zhan},
  journal= {arXiv preprint arXiv:2412.20753},
  year   = {2024}
}
R2 v1 2026-06-28T20:51:44.527Z