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This research introduces "peak state transfer," a novel protocol in continuous-time quantum walks that enables high-fidelity information transport without requiring near-perfect fidelity, allowing for precise timing of transfers. By constructing weighted path graphs with exponentially improved sensitivity over traditional hypercube-based models, the study offers practical candidates for efficient long-distance quantum wires. The work advances the theoretical understanding of qubit networks by establishing spectral characterizations and tight lower bounds on success probability.
Peak state transfer in continuous quantum walks
arXiv:2505.11986v3 Announce Type: replace Abstract: We introduce and study peak state transfer, a notion of high state transfer in qubit networks modeled by continuous-time quantum walks. Unlike perfect or pretty good state transfer, peak state transfer does not require fidelity arbitrarily close to 1, but crucially allows for an explicit determination of the time at which transfer occurs. We provide a spectral characterization of peak state transfer, which allows us to find many examples of peak state transfer, and we also establish tight lower bounds on fidelity and success probability. As a central example, we construct a family of weighted path graphs that admit peak state transfer over arbitrarily long distances with transfer probability approaching $\pi/4 \approx 0.78$. These graphs offer exponentially improved sensitivity over known perfect state transfer examples such as the weighted paths related to hypercubes, making them practical candidates for efficient quantum wires.
Abstract:We introduce and study peak state transfer, a notion of high state transfer in qubit networks modeled by continuous-time quantum walks. Unlike perfect or pretty good state transfer, peak state transfer does not require fidelity arbitrarily close to 1, but crucially allows for an explicit determination of the time at which transfer occurs. We provide a spectral characterization of peak state transfer, which allows us to find many examples of peak state transfer, and we also establish tight lower bounds on fidelity and success probability. As a central example, we construct a family of weighted path graphs that admit peak state transfer over arbitrarily long distances with transfer probability approaching $\pi/4 \approx 0.78$. These graphs offer exponentially improved sensitivity over known perfect state transfer examples such as the weighted paths related to hypercubes, making them practical candidates for efficient quantum wires.
25 pages, 10 figures. V2: Added a discussion about peak state transfer in the family of unweighted graphs from which the weighted graphs were constructed. Also made the paragraph on sensitivity in the introduction more precise and fixed typos in general
Quantum Physics (quant-ph); Combinatorics (math.CO)
arXiv:2505.11986 [quant-ph]
(or arXiv:2505.11986v3 [quant-ph] for this version)
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