Implementing quantum gates through scattering between a static and a flying qubit

TL;DR

This paper explores how to implement two-qubit quantum gates via scattering between a mobile and a static qubit, identifying conditions and parameters that enable entangling gates, especially under resonance with Heisenberg interactions.

Contribution

It demonstrates that quantum gates can be realized through scattering with a static and a flying qubit, highlighting the role of potential barriers and interaction types in gate implementation.

Findings

Gates are achievable with a narrow potential barrier and specific resonance conditions.

Maximum entanglement gates are possible within certain parameter regimes.

Gates show robustness to parameter variations.

Abstract

We investigate whether a two-qubit quantum gate can be implemented in a scattering process involving a flying and a static qubit. To this end, we focus on a paradigmatic setup made out of a mobile particle and a quantum impurity, whose respective spin degrees of freedom couple to each other during a one-dimensional scattering process. Once a condition for the occurrence of quantum gates is derived in terms of spin-dependent transmission coefficients, we show that this can be actually fulfilled through the insertion of an additional narrow potential barrier. An interesting observation is that under resonance conditions the above enables a gate only for isotropic Heisenberg (exchange) interactions and fails for an XY interaction. We show the existence of parameter regimes for which gates able to establish a maximum amount of entanglement can be implemented. The gates are found to be robust to variations of the optimal parameters.