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Perfect quantum state transfer on diamond fractal graphs (1909.08668v2)
Published 18 Sep 2019 in math-ph, cs.IT, math.FA, math.IT, math.MP, math.SP, and quant-ph
Abstract: 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.