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Perfect quantum state transfer on diamond fractal graphs


In the quest for designing novel protocols for quantum information and quantum computation, an important goal is to achieve perfect quantum state transfer for systems beyond the well-known one- dimensional cases, such as 1D spin chains. We use methods from fractal analysis and probability to find a new class of quantum spin chains on fractal-like graphs (known as diamond fractals) which support perfect quantum state transfer and which have a wide range of different Hausdorff and spectral dimensions. The resulting systems are spin networks combining Dyson hierarchical model structure with transverse permutation symmetries of varying order.

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This research was supported in part by the University of Connecticut Research Excellence Program, by DOE Grant DE-SC0010339 and by NSF DMS Grants 1613025 and 2008844. The authors are grateful to Eric Akkermans, Patricia Alonso-Ruiz, and Gabor Lippner for interesting and helpful discussions. The authors are grateful to anonymous referees for suggested improvements to the paper.

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Correspondence to Alexander Teplyaev.

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Derevyagin, M., Dunne, G.V., Mograby, G. et al. Perfect quantum state transfer on diamond fractal graphs. Quantum Inf Process 19, 328 (2020).

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  • Quantum state transfer
  • Quantum computer
  • Spin chain
  • Hierarchical graphs
  • Diamond fractal
  • Hamiltonians with engineered couplings
  • Quantum channels