Can long-range interactions stabilize quantum memory at nonzero temperature?
arXiv:1501.04112 · doi:10.1103/PhysRevA.91.032303
Abstract
A two-dimensional topologically ordered quantum memory is well protected against error if the energy gap is large compared to the temperature, but this protection does not improve as the system size increases. We review and critique some recent proposals for improving the memory time by introducing long-range interactions among anyons, noting that instability with respect to small local perturbations of the Hamiltonian is a generic problem for such proposals. We also discuss some broader issues regarding the prospects for scalable quantum memory in two-dimensional systems.
Title differs from published version as PRA does not allow interrogative titles
References in corpus (44)
- Fault-tolerant quantum computation by anyons
- Anyons in an exactly solved model and beyond
- Topological quantum memory
- String-net condensation: A physical mechanism for topological phases
- Local stabilizer codes in three dimensions without string logical operators
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Spectral Gap and Exponential Decay of Correlations
- Area laws in a many-body localized state and its implications for topological order
- Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
- Localization protected quantum order
- Quantum orders in an exact soluble model
- Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
- Topological quantum order: stability under local perturbations
- Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- Symmetry and Topological Order
- Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
- Stability of Frustration-Free Hamiltonians
- Entanglement and topological entropy of the toric code at finite temperature
- Topological Order at Non-zero Temperature
- Topological order in a 3D toric code at finite temperature
- On thermalization in Kitaev's 2D model
- Quantum logarithmic Sobolev inequalities and rapid mixing
- Fault-tolerant logical gates in quantum error-correcting codes
- Feasibility of self-correcting quantum memory and thermal stability of topological order
- Bringing order through disorder: Localization of errors in topological quantum memories
- Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
- Self-Correcting Quantum Memory in a Thermal Environment
- Quasi-Topological Phases of Matter and Topological Protection
- Local topological order inhibits thermal stability in 2D
- Scaling law for topologically ordered systems at finite temperature
- Localization of Toric Code Defects
- Glauber Dynamics for the mean-field Potts Model
- Disorder-assisted error correction in Majorana chains
- Logical operator tradeoff for local quantum codes
- Enhanced thermal stability of the toric code through coupling to a bosonic bath
- Framework for classifying logical operators in stabilizer codes
- 3-d topological quantum memory with a power-law energy barrier
- Self-Correcting Quantum Memories Beyond the Percolation Threshold
- Non-perturbative gadget for topological quantum codes
- Entropic Barriers for Two-Dimensional Quantum Memories
- Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low temperature regime
- Effective quantum memory Hamiltonian from local two-body interactions
- Novel Topological Phases and Self-Correcting Memories in Interacting Anyon Systems
Cited by in corpus (17)
- Quantum memories at finite temperature
- The upside of noise: engineered dissipation as a resource in superconducting circuits
- Symmetry-protected self-correcting quantum memories
- Passive correction of quantum logical errors in a driven, dissipative system: a blueprint for an analog quantum code fabric
- Cellular automaton decoders of topological quantum memories in the fault tolerant setting
- Fault-Tolerant Quantum Error Correction for non-Abelian Anyons
- Topological Order and Memory Time in Marginally Self-Correcting Quantum Memory
- Anyonic self-induced disorder in a stabilizer code: quasi-many body localization in a translational invariant model
- Symmetry protected self correcting quantum memory in three space dimensions
- Quantum memories with zero-energy Majorana modes and experimental constraints
- Self correction requires Energy Barrier for Abelian quantum doubles
- Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise
- Exponential Lifetime Improvement in Topological Quantum Memories
- Self-correction in Wegner's 3D Ising lattice gauge theory
- Stability of ground state degeneracy to long-range interactions
- Self-correction from higher-form symmetry protection on a boundary
- Layer codes as partially self-correcting quantum memories