01560nas a2200157 4500008004100000245005000041210005000091260001400141520111200155100001801267700001601285700001601301700002501317700002301342856003701365 2023 eng d00aBounds on Autonomous Quantum Error Correction0 aBounds on Autonomous Quantum Error Correction c8/30/20233 a

Autonomous quantum memories are a way to passively protect quantum information using engineered dissipation that creates an "always-on'' decoder. We analyze Markovian autonomous decoders that can be implemented with a wide range of qubit and bosonic error-correcting codes, and derive several upper bounds and a lower bound on the logical error rate in terms of correction and noise rates. For many-body quantum codes, we show that, to achieve error suppression comparable to active error correction, autonomous decoders generally require correction rates that grow with code size. For codes with a threshold, we show that it is possible to achieve faster-than-polynomial decay of the logical error rate with code size by using superlogarithmic scaling of the correction rate. We illustrate our results with several examples. One example is an exactly solvable global dissipative toric code model that can achieve an effective logical error rate that decreases exponentially with the linear lattice size, provided that the recovery rate grows proportionally with the linear lattice size.

1 aShtanko, Oles1 aLiu, Yu-Jie1 aLieu, Simon1 aGorshkov, Alexey, V.1 aAlbert, Victor, V. uhttps://arxiv.org/abs/2308.1623301489nas a2200133 4500008004100000245007300041210006900114260001300183520106500196100001601261700001601277700002501293856003701318 2023 eng d00aCandidate for a passively protected quantum memory in two dimensions0 aCandidate for a passively protected quantum memory in two dimens c3/2/20233 a

An interesting problem in the field of quantum error correction involves finding a physical system that hosts a ``passively protected 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, the photonic-Ising model, which appears to passively 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. We also discuss possible ways to realize the photonic-Ising model.

1 aLieu, Simon1 aLiu, Yu-Jie1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2205.0976701388nas a2200133 4500008004100000245006900041210006800110260001400178520096800192100001601160700001601176700002501192856003701217 2022 eng d00aCandidate for a self-correcting quantum memory in two dimensions0 aCandidate for a selfcorrecting quantum memory in two dimensions c5/19/20223 a

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. 

1 aLieu, Simon1 aLiu, Yu-Jie1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2205.09767