Quantum error correction and large
arXiv:2008.12869 · doi:10.21468/SciPostPhys.11.5.094
Abstract
In recent years quantum error correction(QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this paper is to fill this gap by studying the error correcting properties of the fermionic sector of various large theories. Specifically we examine matrix quantum mechanics and 3-rank tensor theories. Both of these theories contain large gauge groups. We argue that gauge singlet states indeed form a quantum error correcting code. Our considerations are based purely on large analysis and do not appeal to a particular form of Hamiltonian or holography.
arXiv commentv1: 21 pages + appendices, 6 figures. v2: typos corrected. v3: minor corrections
References in corpus (50)
- M Theory As A Matrix Model: A Conjecture
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Decoherence Free Subspaces for Quantum Computation
- Comments on the Sachdev-Ye-Kitaev model
- Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
- Supergravity and The Large N Limit of Theories With Sixteen Supercharges
- Symmetries and Strings in Field Theory and Gravity
- A Theory of Quantum Error-Correcting Codes
- A class of quantum many-body states that can be efficiently simulated
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Bulk Locality and Quantum Error Correction in AdS/CFT
- The Spectrum in the Sachdev-Ye-Kitaev Model
- Criticality, the area law, and the computational power of PEPS
- Classical simulation of quantum many-body systems with a tree tensor network
- Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
- Holographic representation of local bulk operators
- Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
- Holographic duality from random tensor networks
- Restrictions on Transversal Encoded Quantum Gate Sets
- Causality & holographic entanglement entropy
- The Ryu-Takayanagi Formula from Quantum Error Correction
- Capacities of Quantum Erasure Channels
- Uncolored Random Tensors, Melon Diagrams, and the SYK Models
- A toy model for the AdS/CFT correspondence
- Reversing quantum dynamics with near-optimal quantum and classical fidelity
- Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
- Constraints on symmetry from holography
- Approximate quantum error correction can lead to better codes
- Eternal traversable wormhole
- Causal Holographic Information
- Many Body Scars as a Group Invariant Sector of Hilbert Space
- Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
- Random Tensor Models
- M-Theory and the Light Cone
- Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography
- Spectra of Operators in Large Tensor Models
- Precision lattice test of the gauge/gravity duality at large-
- Continuous symmetries and approximate quantum error correction
- Bulk-Boundary Duality, Gauge Invariance, and Quantum Error Correction
- To gauge or not to gauge?
- Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics
- Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames
- Construction of bosonic string theory on infinitely curved Anti-de Sitter space
- The Large N Harmonic Oscillator as a String Theory
- Gauged And Ungauged: A Nonperturbative Test
- Scrambling and decoding the charged quantum information
- Approximate quantum error correction
- Areas and entropies in BFSS/gravity duality
- Lightcone Quantization of String Theory Duals of Free Field Theories
- The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories