Local stabilizer codes in three dimensions without string logical operators
By Jeongwan Haah. 2011
584 citations recorded by the source corpus.
We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have stringlike logical operators, which make the codes non-self-correcting. We introduce a notion of “logical string segments” to avoid difficulties in defining one-dimensional objects in discrete lattices. We prove that every stringlike logical operator of our code can be deformed to a disjoint union of short segments, each of which is in the stabilizer group. The code has surfacelike logical operators whose partial implementation has unsatisfied stabilizers along its boundary.
Subfields: Artificial Intelligence, Computer Networks and Communications, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/f28efab1a59c1785831930c139ec4db5b83ec148
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In Artificial Intelligence
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Citations in the corpus
- Fracton phases of matter (2020, methodology): “How can we practically manipulate fractons in some useful way? It has been widely suggested that the properties of fractons will be useful for the purpose of quantum information storage [2, 16–18], but we lack any concrete roadmap for the precise implementation of this proposal.”
- Quantum computing and the entanglement frontier (2012, unknown): “69,70 9.”
- Asymptotically good Quantum and locally testable classical LDPC codes (2021, methodology): “In this work, we consider several new families of classical and quantum LDPC codes of constant rate based on the introduced recently lifted product construction [44], which generalizes many known constructions of quantum LDPC codes [24, 25, 34, 38, 49, 52].”
- Generalized Symmetries in Condensed Matter (2022, unknown): “A subsystemsymmetry-based understanding of Haah’s code (85) appears in (86).”
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality (2016, methodology): “Fractons may be used to build a robust, finite-temperature quantum memory, as theoretically demonstrated for Haah’s code [16,22].”
- Quantum error correction for quantum memories (2013, unknown): “The first example of such a 3D code was the Haah code with E barrier ≥ c log L (Bravyi and Haah, 2011; Haah, 2011) for which all logical operators are fractal (instead of string-or surfacelike).”
- Quantum memories at finite temperature (2014, methodology): “We remark also on the work due to Haah and Preskill in Ref.”
- Localization from Hilbert space shattering: From theory to physical realizations (2020, background): “Most of this work will focus on models inspired by fracton systems [28–34] in which excitations are known to exhibit restricted mobility.”
- Strong resilience of topological codes to depolarization (2012, background): “Our best strategy then is to classify the remaining, nondistinguishable errors according to their effect on the encoded logical information and undo the effects of the most probable equivalence class E.”
- Towards Classification of Fracton Phases: The Multipole Algebra (2018, methodology): “6 S. Vijay, J. Haah, and L. Fu, Physical Review B 92, 235136 (2015).”
- Fractons (2018, background): “[8] Jeongwan Haah, “Local stabilizer codes in three dimensions without string logical operators,””
- Quantum Information Meets Quantum Matter (2015, methodology): “eir corresponding notation used for quantum circuits in quantum computing literatures. Readers interested in quantum circuits should refer to textbooks in quantum computing, for instance Chapter 4 in [11]. It is not the goal of this chapter to be involved too much with quantum circuit theory. Instea”
- Fracton hydrodynamics (2020, background): “[14] Jeongwan Haah, “Local stabilizer codes in three dimensions without string logical operators,” Physical Review A 83, 042330 (2011).”