Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape

Understand

We analyze the role of coherent tunneling that gives rise to bands of delocalized quantum states providing a coherent pathway for population transfer (PT) between computational states with similar energies.

• Given an energy function ${\cal E}(z)$ of a binary optimization problem and a bit-string $z_i$ with atypically low energy, our goal is to find other bit-strings with energies within a narrow window around ${\cal E}(z_i)$.
• We study PT due to quantum evolution under a transverse field $B_\perp$ of an n-qubit system that encodes ${\cal E}(z)$.
• We focus on a simple yet nontrivial model: $M$ randomly chosen &#34;marked&#34; bit-strings ($2^n \gg M$) are assigned energies in the interval ${\cal E}(z)\in[-n -W/2, n + W/2]$ with $W << B_\perp$, while the rest of the states are assigned energy $0$.