Two-Particle Scattering on Non-Translation Invariant Line Lattices

• URL: http://arxiv.org/abs/2303.04342v2
• Date: Tue, 26 Mar 2024 17:20:37 GMT
• Title: Two-Particle Scattering on Non-Translation Invariant Line Lattices
• Authors: Luna Lima e Silva, Daniel Jost Brod,
• Abstract summary: Quantum walks have been used to develop quantum algorithms since their inception. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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.

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