Spectral surgery on a uniform XX chain yields analytic spin chains that interpolate between uniform and Krawtchouk chains and achieve good-fidelity state transfer with bounded couplings.
Incorporating Encoding into Quantum System Design
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When creating a quantum system whose natural dynamics provide useful computational operations, designers have two key tools at their disposal: the (constrained) choice of both the Hamiltonian and the the initial state of the system (an encoding). Typically, we fix the design, and utilise encodings post factum to tolerate experimental imperfections. In this paper, we describe a vital insight that incorporates encoding into the design process, with radical consequences. This transforms the study of perfect state transfer from the unrealistic scenario of specifying the Hamiltonian of an entire system to the far more realistic situation of being given a Hamiltonian over which we had no choice in the design, and designing time control of just two parameters to still achieve perfect transfer.
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Spectral surgery and high-fidelity quantum state transfer in $XX$ chains
Spectral surgery on a uniform XX chain yields analytic spin chains that interpolate between uniform and Krawtchouk chains and achieve good-fidelity state transfer with bounded couplings.