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Related papers: Topological quantum error correction in the Kitaev…

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With the advancement in synthesizing and analyzing Kitaev materials, the Kitaev-Heisenberg model on the honeycomb lattice has attracted a lot of attention in the last few years. Several variations, which include additional anisotropic…

Strongly Correlated Electrons · Physics 2018-08-15 Darshan G. Joshi

Kitaev's toric code is arguably the most studied quantum code and is expected to be implemented in future generations of quantum computers. The renormalisation decoders introduced by Duclos-Cianci and Poulin exhibit one of the best…

Quantum Physics · Physics 2023-09-22 Wouter Rozendaal , Gilles Zémor

In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling…

Quantum Physics · Physics 2013-05-29 Su-Peng Kou

We study the quantum phase transition between Abelian and non-Abelian phases in an extended Kitaev spin model on the honeycomb lattice, where the periodic boundary condition is applied by placing the lattice on a torus. Our analytical…

Statistical Mechanics · Physics 2015-05-13 Xiao-Feng Shi , Yue Yu , J. Q. You , Franco Nori

Topological stabilizer codes, such as the toric and surface codes, are leading candidates for fault-tolerant quantum computation. While their decodability under stochastic noise has been extensively studied, the effects of coherent errors,…

Statistical Mechanics · Physics 2026-04-13 Zhou Yang , Andreas W. W. Ludwig , Chao-Ming Jian

We analyze the long time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is…

Quantum Physics · Physics 2008-07-11 E. Novais , Eduardo R. Mucciolo , Harold U. Baranger

Compass models are theories of matter in which the couplings between the internal spin (or other relevant field) components are inherently spatially (typically, direction) dependent. Compass-type interactions appear in diverse physical…

Strongly Correlated Electrons · Physics 2013-05-02 Zohar Nussinov , Jeroen van den Brink

Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…

Quantum Physics · Physics 2025-05-20 Oliver Weissl , Evgenii Egorov

From the perspective of quantum many-body physics, the Floquet code of Hastings and Haah can be thought of as a measurement-only version of the Kitaev honeycomb model where a periodic sequence of two-qubit XX, YY, and ZZ measurements…

Quantum Physics · Physics 2023-11-16 Guo-Yi Zhu , Simon Trebst

Topologically-ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models…

Quantum Physics · Physics 2025-02-13 Yaodong Li , Nicholas O'Dea , Vedika Khemani

It is well-known that the partition function of a classical spin model can be mapped to a quantum entangled state where some properties on one side can be used to find new properties on the other side. However, the consequences of the…

Quantum Physics · Physics 2019-05-13 Mohammad Hossein Zarei , Afshin Montakhab

The ground state degeneracy of topologically ordered gapped Hamiltonians is the bedrock for self-correcting quantum memories, which are unfortunately not stable away from equilibrium even at zero temperature. This plague precludes practical…

Quantum Physics · Physics 2025-02-12 Yu Zeng , Alioscia Hamma , Yu-Ran Zhang , Jun-Peng Cao , Heng Fan , Wu-Ming Liu

Kitaev's toric code has become one of the most studied models in physics and is highly relevant to the fields of both quantum error correction and condensed matter physics. Most notably, it is the simplest known model hosting an extended,…

Quantum Physics · Physics 2026-02-17 Simon M. Linsel , Lode Pollet , Fabian Grusdt

The Kitaev honeycomb model provides a paradigmatic example of an exactly solvable quantum spin liquid (QSL), in which the spin degrees of freedom fractionalize into itinerant Majorana fermions coupled to a static background of…

Strongly Correlated Electrons · Physics 2024-06-28 Vitor Dantas , Wen-Han Kao , Natalia B. Perkins

The Hamiltonian model of quantum error correction code in the literature is often constructed with the help of its stabilizer formalism. But there have been many known examples of nonadditive codes which are beyond the standard quantum…

Quantum Physics · Physics 2008-01-28 Yong Zhang

We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations. The effective low-energy Hamiltonian is found to be an extended toric code with interacting anyons. High-energy…

Other Condensed Matter · Physics 2008-05-06 K. P. Schmidt , S. Dusuel , J. Vidal

Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the…

Quantum Physics · Physics 2026-03-24 Luca Menti , Francisco Lázaro

A physical realization of self correcting quantum code would be profoundly useful for constructing a quantum computer. In this theoretical work, we provide a partial solution to major challenges preventing self correcting quantum code from…

Quantum Physics · Physics 2015-07-01 Eliot Kapit , John T. Chalker , Steven H. Simon

The Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation. However, direct methods to increase its logical dimensions, such as lattice surgery or introducing…

Quantum Physics · Physics 2025-10-09 Zijian Liang , Ke Liu , Hao Song , Yu-An Chen

We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…

Quantum Physics · Physics 2025-05-09 Louis Fraatz , Amit Jamadagni , Hendrik Weimer