Universal quantum computation in waveguide QED using decoherence free subspaces

Abstract

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