An interesting problem in the field of quantum error correction involves finding a physical system that hosts a "self-correcting quantum memory," defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model which appears to self correct against both bit-flip and phase-flip errors in two dimensions: A square lattice composed of photonic "cat qubits" coupled via dissipative terms which tend to fix errors locally. Inspired by the presence of two distinct Z2-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips.

%8 5/19/2022 %G eng %U https://arxiv.org/abs/2205.09767 %0 Journal Article %J Phys. Rev. B %D 2022 %T Kramers' degeneracy for open systems in thermal equilibrium %A Simon Lieu %A Max McGinley %A Oles Shtanko %A Nigel R. Cooper %A Alexey V. Gorshkov %B Phys. Rev. B %V 105 %P L121104 %8 3/10/2022 %G eng %U https://arxiv.org/abs/2105.02888 %N 12 %R https://doi.org/10.1103/PhysRevB.105.L121104 %0 Journal Article %D 2021 %T Clustering of steady-state correlations in open systems with long-range interactions %A Andrew Y. Guo %A Simon Lieu %A Minh C. Tran %A Alexey V. Gorshkov %XLieb-Robinson bounds are powerful analytical tools for constraining the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In experimental systems, however, interactions with the environment cannot generally be ignored, and the extension of Lieb-Robinson bounds to dissipative systems which evolve non-unitarily in time remains an open challenge. In this work, we prove two Lieb-Robinson bounds that constrain the dynamics of open quantum systems with long-range interactions that decay as a power-law in the distance between particles. Using a combination of these Lieb-Robinson bounds and mixing bounds which arise from "reversibility" -- naturally satisfied for thermal environments -- we prove the clustering of correlations in the steady states of open quantum systems with long-range interactions. Our work provides an initial step towards constraining the steady-state entanglement structure for a broad class of experimental platforms, and we highlight several open directions regarding the application of Lieb-Robinson bounds to dissipative systems.

%8 10/28/2021 %G eng %U https://arxiv.org/abs/2110.15368 %0 Journal Article %J Phys. Rev. Lett. %D 2020 %T Symmetry breaking and error correction in open quantum systems %A Simon Lieu %A Ron Belyansky %A Jeremy T. Young %A Rex Lundgren %A Victor V. Albert %A Alexey V. Gorshkov %XSymmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system---a Lindbladian---a unitary symmetry can be imposed in a "weak" or a "strong" way. We characterize the possible Zn symmetry breaking transitions for both cases. In the case of Z2, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially-protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correctio

%B Phys. Rev. Lett. %V 125 %P 240405 %8 8/6/2020 %G eng %U https://arxiv.org/abs/2008.02816 %R https://doi.org/10.1103/PhysRevLett.125.240405