Self-dual random-plaquette gauge model and the quantum toric code

Abstract

We study the four-dimensional Z_2 random-plaquette lattice gauge theory as a model of topological quantum memory, the toric code in particular. In this model, the procedure of quantum error correction works properly in the ordered (Higgs) phase, and phase boundary between the ordered (Higgs) and disordered (confinement) phases gives the accuracy threshold of error correction. Using self-duality of the model in conjunction with the replica method, we show that this model has exactly the same mathematical structure as that of the two dimensional random-bond Ising model, which has been studied very extensively. This observation enables us to derive a conjecture on the exact location of the multicritical point (accuracy threshold) of the model, p_c=0.889972..., and leads to several nontrivial results including bounds on the accuracy threshold in three dimensions.

23 pages, 13 figures

References in corpus (14)

• Fault-tolerant quantum computation by anyons
• Topological quantum memory
• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• The two-dimensional random-bond Ising model, free fermions and the network model
• Nishimori point in the 2D +/- J random-bond Ising model
• The Cluster Processor: New Results
• Duality and Multicritical Point of Two-Dimensional Spin Glasses
• Universality, frustration and conformal invariance in two-dimensional random Ising magnets
• High Temperature Expansion Study of the Nishimori multicritical Point in Two and Four Dimensions
• Symmetry, complexity and multicritical point of the two-dimensional spin glass
• New Algorithm of the Finite Lattice Method for the High-temperature Expansion of the Ising Model in Three Dimensions
• Correlation--function distributions at the Nishimori point of two-dimensional Ising spin glasses
• Z_N Gauge Theories on a Lattice and Quantum Memory
• New algorithm of the high-temperature expansion for the Ising model in three dimensions

Cited by in corpus (26)

• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Homological Error Correction: Classical and Quantum Codes
• Feasibility of self-correcting quantum memory and thermal stability of topological order
• Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory
• Single-shot error correction of three-dimensional homological product codes
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Locations of multicritical points for spin glasses on regular lattices
• Scalable Neural Network Decoders for Higher Dimensional Quantum Codes
• Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices
• Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic
• Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture
• Overfrustrated and Underfrustrated Spin-Glasses in d=3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d=2
• Multicritical Point Relations in Three Dual Pairs of Hierarchical-Lattice Ising Spin-Glasses
• On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses
• Analytical evidence for the absence of spin glass transition on self-dual lattices
• Renormalization group decoder for a four-dimensional toric code
• Reentrant and Forward Phase Diagrams of the Anisotropic Three-Dimensional Ising Spin Glass
• A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)
• Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices
• Renormalization Group on hierarchical lattices in finite dimensional disordered Ising and Blume-Emery-Griffiths Models
• Duality in finite-dimensional spin glasses
• Self-Duality and Phase Structure of the 4D Random-Plaquette Z_2 Gauge Model
• Low-temperature coherence properties of Z_2 quantum memory
• The Implications of Ignorance for Quantum Error Correction Thresholds
• Population annealing with topological defect driven nonlocal updates for spin systems with quenched disorder
• Topological approach toward quantum codes with realistic physical constraints