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.

UR - https://arxiv.org/abs/2205.09767 ER - TY - JOUR T1 - Kramers' degeneracy for open systems in thermal equilibrium JF - Phys. Rev. B Y1 - 2022 A1 - Simon Lieu A1 - Max McGinley A1 - Oles Shtanko A1 - Nigel R. Cooper A1 - Alexey V. Gorshkov VL - 105 U4 - L121104 UR - https://arxiv.org/abs/2105.02888 CP - 12 U5 - https://doi.org/10.1103/PhysRevB.105.L121104 ER - TY - JOUR T1 - Clustering of steady-state correlations in open systems with long-range interactions Y1 - 2021 A1 - Andrew Y. Guo A1 - Simon Lieu A1 - Minh C. Tran A1 - Alexey V. Gorshkov AB -Lieb-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.

UR - https://arxiv.org/abs/2110.15368 ER - TY - JOUR T1 - Symmetry breaking and error correction in open quantum systems JF - Phys. Rev. Lett. Y1 - 2020 A1 - Simon Lieu A1 - Ron Belyansky A1 - Jeremy T. Young A1 - Rex Lundgren A1 - Victor V. Albert A1 - Alexey V. Gorshkov AB -Symmetry-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

VL - 125 U4 - 240405 UR - https://arxiv.org/abs/2008.02816 U5 - https://doi.org/10.1103/PhysRevLett.125.240405 ER -