The paper shows numerically that a variational quantum algorithm with an uncorrelated ansatz transfers a spin excitation across a chain in time close to the (N-1)/(2J0) bound, and proposes a W1-based control optimality metric to evaluate hybrid quantum-classical control.
A Note on the Speed of Perfect State Transfer
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abstract
In Phys. Rev. A 74, 030303 (2006), Yung showed that for a one-dimensional spin chain of length $N$ and maximum coupling strength $J_{\max}$, the time $t_0$ for a quantum state to transfer from one end of the chain to another is bounded by $J_{\max} t_0\geq\pi N/4$ (even $N$) and $J_{\max} t_0\geq\pi\sqrt{N^2-1}/4$ (odd $N$). The proof for even $N$ was elegant, but the proof for odd $N$ was less so. This note provides a proof for the odd $N$ case that is simpler, and more in keeping with the proof for the even case.
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Optimal Control by Variational Quantum Algorithms
The paper shows numerically that a variational quantum algorithm with an uncorrelated ansatz transfers a spin excitation across a chain in time close to the (N-1)/(2J0) bound, and proposes a W1-based control optimality metric to evaluate hybrid quantum-classical control.