Related Experiment Video
Updated: Aug 16, 2025
08:55
Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
8.6K
Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
Hao Song1,2,3, Janik Schönmeier-Kromer4,5, Ke Liu4,5
1CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Physical Review Letters
|December 23, 2022
Summary
Fracton codes offer a novel approach to quantum error correction, demonstrating significantly higher error thresholds than traditional topological codes. This makes fracton phases promising for robust quantum memory development.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
- Quantum Computing
Background:
- Fracton models represent novel gapped quantum phases beyond conventional topological order.
- These phases feature immobile excitations, offering unique properties for quantum technologies.
Purpose of the Study:
- To calculate optimal error thresholds for quantum error correcting codes based on fracton models.
- To investigate the potential of fracton phases as quantum memory platforms.
Main Methods:
- Mapping error correction for bit-flip and phase-flip noise to statistical models with Ising variables and random multibody couplings.
- Utilizing large-scale parallel tempering Monte Carlo simulations to generate disorder-temperature phase diagrams.
- Analyzing subsystem symmetries distinct from global symmetries.
Main Results:
- The X-cube fracton code exhibits a minimum error threshold of 7.5%, substantially higher than 3D topological codes like the toric code (3.3%) and color code (1.9%).
- Absence of glass order at the Nishimori line was predicted.
- The study identified unconventional subsystem symmetries in the error-correction models.
Conclusions:
- Fracton codes demonstrate superior error resilience compared to existing 3D topological codes.
- The findings highlight the significant potential of fracton phases for building stable and efficient quantum memory systems.
Related Concept Videos
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
1.1K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.1K
01:34Woodward–Hoffmann Selection Rules and Microscopic Reversibility
3.2K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
3.2K
01:08Spin–Spin Coupling Constant: Overview
982
In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
982
01:10Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
1.4K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
1.4K
01:14Atomic Nuclei: Nuclear Spin State Population Distribution
1.1K
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
1.1K
02:46Crystal Field Theory - Tetrahedral and Square Planar Complexes
43.7K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
43.7K