Universal Quantum Computation in Waveguide QED using Decoherence Free Subspaces

TL;DR

This paper demonstrates how to achieve universal quantum computation within Decoherence Free Subspaces in Waveguide QED by using controlled drivings and analyzing the system's dynamics.

Contribution

It introduces a method to perform universal quantum gates within DFS in Waveguide QED using single-site drivings and Liouvillian perturbation theory analysis.

Findings

Effective coherent evolution within DFS enables universal quantum gates.

Scaling behavior analyzed with Purcell Factor and control imperfections.

Comparison with previous atomic cavity proposals shows advantages.

Abstract

The interaction of quantum emitters with one-dimensional photon-like reservoirs induces strong and long-range dissipative couplings that give rise to the emergence of so-called Decoherence Free Subspaces (DFS) which are decoupled from dissipation. When introducing weak perturbations on the emitters, e.g., driving, the strong collective dissipation enforces an effective coherent evolution within the DFS. In this work, we show explicitly how by introducing single-site resolved drivings, we can use the effective dynamics within the DFS to design a universal set of one and two-qubit gates within the DFS of two-level atom-like systems. Using Liouvillian perturbation theory we calculate the scaling with the relevant figures of merit of the systems, such as the Purcell Factor and imperfect control of the drivings. Finally, we compare our results with previous proposals using atomic $\Lambda$ systems in leaky cavities.