Stabilizer codes allow for non-local encoding and processing of quantum information. Deformations of stabilizer surface codes introduce new and non-trivial geometry, in particular leading to emergence of long sought after objects known as projective Ising non-Abelian anyons. Braiding of such anyons is a key ingredient of topological quantum computation. We suggest a simple and systematic approach to construct effective unitary protocols for braiding, manipulation and readout of non-Abelian anyons and preparation of their entangled states. We generalize the surface code to a more generic graph with vertices of degree 2, 3 and 4. Our approach is based on the mapping of the stabilizer code defined on such a graph onto a model of Majorana fermions charged with respect to two emergent gauge fields. One gauge field is akin to the physical magnetic field. The other one is responsible for emergence of the non-Abelian anyonic statistics and has a purely geometric origin. This field arises from assigning certain rules of orientation on the graph known as the Kasteleyn orientation in the statistical theory of dimer coverings. Each 3-degree vertex on the graph carries the flux of this "Kasteleyn" field and hosts a non-Abelian anyon. In our approach all the experimentally relevant operators are unambiguously fixed by locality, unitarity and gauge invariance. We illustrate the power of our method by making specific prescriptions for experiments verifying the non-Abelian statistics.
Topological stabilizer models on continuous variables
Dahlem Center for Complex Quantum Systems, Freie Universität Berlin（柏林自由大学达勒姆复杂量子系统中心）；Perimeter Institute for Theoretical Physics（理论物理 perimeter 研究所）；Department of Physics, Yale University（耶鲁大学物理系）；Department of Physics and Astronomy, Purdue University（普渡大学物理与天文学系）；Purdue Quantum Science and Engineering Institute, Purdue University（普渡大学普渡量子科学与工程研究所）；School of Physics, University of Sydney（悉尼大学物理学院）
Operator algebra and algorithmic construction of boundaries and defects in (2+1)D topological Pauli stabilizer codes
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Center of Mathematical Sciences and Applications, Harvard University（哈佛大学数学科学应用中心）；Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算机科学联合中心）
Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；C. N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学陈省身理论物理研究所）
Resolving spurious topological entanglement entropy in stabilizer codes
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料科学中心）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Center of Mathematical Sciences and Applications, Harvard University（哈佛大学数学科学应用中心）；Department of Mathematics, Harvard University（哈佛大学数学系）
Intrinsic mixed state topological order in a stabilizer system under stochastic decoherence: Strong-to-weak spontaneous symmetry breaking from percolation point of view
Symmetry-enriched topological order and quasifractonic behavior in $\mathbb{Z}_N$ stabilizer codes
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Max-Planck-Institute of Quantum Optics（马克斯·普朗克量子光学研究所）
Anyon-Impurity Bound States in Quantum-Engineered Fractional Chern Insulators
International Solvay Institutes（国际索尔维研究所）；Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（布鲁塞尔自由大学非线性现象与复杂系统中心）；Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München（慕尼黑大学物理系及阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
Pauli stabilizer formalism for topological quantum field theories and generalized statistics
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；School of Natural Sciences, Institute for Advanced Study, Princeton（普林斯顿高等研究院自然科学院）；Department of Mathematics, King’s College London（伦敦国王学院数学系）
Enhanced thermal stability of the toric code through coupling to a bosonic bath
我们提出并研究了一个量子存储器模型，该模型具有自校正特性，并且在非零温度下寿命随系统尺寸任意增长。这是通过将2D L x L复曲面代码局部耦合到立方晶格上跳跃的3D玻色子浴来实现的。当复曲面代码的稳定算子耦合到玻色子的位移算子时，我们通过极化子变换精确地求解模型，并表明创建任意子的能量惩罚随L线性增长。当复曲面码的稳定子算符与玻色密度算符耦合时，我们利用微扰理论证明了任意子的能量罚与ln（L）成比例。对于给定的误差模型，这些能量损失导致所存储的量子信息的寿命分别随L指数地和多项式地增长。此外，我们展示了如何选择一个适当的耦合方案，以阻碍跳跃的任意子（而不仅仅是他们的创造）与能量障碍是相同的顺序作为任意子创建间隙。我们认为，一个复曲面代码耦合到一个3D海森堡铁磁体实现我们的模型在其低能量部门。最后，我们讨论了在扰动存在下拓扑序的稳定性这一微妙的问题。虽然我们没有得到严格的证明拓扑顺序，我们提出了启发式的参数表明，拓扑顺序保持不变时，扰动算子作用于环面代码自旋耦合到玻色子环境。
