Bounds on Autonomous Quantum Error Correction
arXiv:2308.16233 · doi:10.22331/q-2025-07-22-1804
Abstract
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. These bounds suggest that, in general, there is always a correction rate, possibly size-dependent, above which autonomous memories exhibit arbitrarily long coherence times. For any given autonomous memory, size dependence of this correction rate is difficult to rule out: we point to common scenarios where autonomous decoders that stochastically implement active error correction must operate at 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.
48 pages, 8 figures, 1 table
References in corpus (39)
- Anyons in an exactly solved model and beyond
- Topological quantum memory
- Quantum Error Correction for Quantum Memories
- Local stabilizer codes in three dimensions without string logical operators
- Confining the state of light to a quantum manifold by engineered two-photon loss
- Real-time quantum error correction beyond break-even
- New class of quantum error-correcting codes for a bosonic mode
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
- The computational complexity of PEPS
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- Continuous quantum error correction via quantum feedback control
- Exponential suppression of bit-flips in a qubit encoded in an oscillator
- Quantum memories at finite temperature
- The power of quantum systems on a line
- Quantum computing with rotation-symmetric bosonic codes
- Quantum memories based on engineered dissipation
- Topological Order at Non-zero Temperature
- Thresholds for topological codes in the presence of loss
- Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
- Coherent oscillations inside a quantum manifold stabilized by dissipation
- On thermalization in Kitaev's 2D model
- Tailoring surface codes for highly biased noise
- Fault-tolerant logical gates in quantum error-correcting codes
- Commuting Pauli Hamiltonians as maps between free modules
- Feasibility of self-correcting quantum memory and thermal stability of topological order
- Continuous quantum error correction by cooling
- Cellular-automaton decoders with provable thresholds for topological codes
- Self-Correcting Quantum Memory in a Thermal Environment
- Local topological order inhibits thermal stability in 2D
- Stability of local quantum dissipative systems
- Rapid thermalization of spin chain commuting Hamiltonians
- Implementation-independent sufficient condition of the Knill-Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation
- Logical operator tradeoff for local quantum codes
- Passive correction of quantum logical errors in a driven, dissipative system: a blueprint for an analog quantum code fabric
- Area law for fixed points of rapidly mixing dissipative quantum systems
- An optimal dissipative encoder for the toric code
- Novel Topological Phases and Self-Correcting Memories in Interacting Anyon Systems
- Thermalization in Kitaev's quantum double models via Tensor Network techniques