Quantum walks have been used to develop quantum algorithms since their inception, and can be seen as an alternative to the usual circuit model; combining single-particle quantum walks on sparse graphs with two-particle scattering on a line lattice is sufficient to perform universal quantum computation. In this work we solve the problem of two-particle scattering on the line lattice for a family of interactions without translation invariance, recovering the Bose-Hubbard interaction as the limiting case. Due to its generality, our systematic approach lays the groundwork to solve the more general problem of multi-particle scattering on general graphs, which in turn can enable design of different or simpler quantum gates and gadgets. As a consequence of this work, we show that a CPHASE gate can be achieved with high fidelity when the interaction acts only on a small portion of the line graph.

中文翻译：

---

非平移不变线晶格上的二粒子散射

量子行走自诞生以来就被用来开发量子算法，并且可以被视为通常电路模型的替代方案；将稀疏图上的单粒子量子行走与线晶格上的双粒子散射相结合足以执行通用量子计算。在这项工作中，我们解决了一系列没有平移不变性的相互作用的线晶格上的两粒子散射问题，恢复了玻色-哈伯德相互作用作为极限情况。由于其通用性，我们的系统方法为解决一般图上的多粒子散射这一更普遍的问题奠定了基础，这反过来又可以实现不同或更简单的量子门和小工具的设计。这项工作的结果是，我们表明，当交互作用仅作用于线图的一小部分时，可以以高保真度实现 CPHASE 门。