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In a recent work (arXiv:2207.01954), we showed that a uniformly coupled chaincould be symmetrically extended by engineered spin chains in such a way that wecould choose part of the spectrum of the overall system. When combined with anencoding that avoids the uncontrolled eigenvalues, this resulted in thepossibility of achieving a range of tasks such as perfect quantum statetransfer. In this paper, we apply the same strategy to a much broader range ofinitial systems - arbitrary chains, and even coupled networks of spins - whileproviding guarantees on the existence of solutions.

Encoded State Transfer: Beyond the Uniform Chain