Spectral surgery and high-fidelity quantum state transfer in XX chains

We consider an inhomogeneous XX spin chain which interpolates between the Krawtchouk one with perfect state transfer and the homogeneous XX chain. This model can be used to perform qubit state transfer with sufficiently high fidelity. The advantage of this model with respect to the Krawtchouk chain is that while maintaining high transfer fidelity, the disparity between the largest and the smallest coupling strengths grows much more slowly as the number of sites increases. The construction is fully analytic and is based on spectral surgery transformations of the homogeneous chain. An explicit lower bound on the transfer amplitude is derived; it provides a readout time in closed form and quantifies the trade-off between fidelity and coupling strengths.