两能级量子系统，量子比特，并不是量子计算的唯一基础。量子点，d能级量子系统，作为量子信息的基本载体，具有优势。我们证明了色码，一类具有显著横截性的拓扑量子码，可以推广到qudit范式。在最近的发展中，人们发现，在三维空间中，量子比特色码可以支持横向非Clifford门，并且在更高的空间维度中，可以找到额外的非Clifford门，饱和Bravyi和König的界限[Phys. Rev. Lett. 110，170503（2013）]。此外，通过使用规范固定技术，可以实现一组有效的Clifford门，从而消除了对状态蒸馏的需要。我们表明，qudit颜色代码可以支持qudit类似物的这些门，并表明，在更高的空间维度的颜色代码可以支持一个相位门从更高层次的Clifford层次结构，可以证明饱和Bravyi和柯尼希的约束，但在所有有限的特殊情况下。所使用的方法是Bravyi和Haah的三正交矩阵方法[Phys.Rev.A86052329（2012）]的概括，其可能是独立感兴趣的。为了完整性，我们明确地表明，量子色码推广到规范色码，并分享了许多有利的性质，他们的量子比特同行。
英文摘要：
Two-level quantum systems, qubits, are not the only basis for quantum computation. Advantages exist in using qudits, d-level quantum systems, as the basic carrier of quantum information. We show that color codes, a class of topological quantum codes with remarkable transversality properties, can be generalized to the qudit paradigm. In recent developments it was found that in three spatial dimensions a qubit color code can support a transversal non-Clifford gate, and that in higher spatial dimensions additional non-Clifford gates can be found, saturating Bravyi and König's bound [Phys. Rev. Lett. 110, 170503 (2013)]. Furthermore, by using gauge fixing techniques, an effective set of Clifford gates can be achieved, removing the need for state distillation. We show that the qudit color code can support the qudit analogues of these gates, and show that in higher spatial dimensions a color code can support a phase gate from higher levels of the Clifford hierarchy which can be proven to saturate Bravyi and König's bound in all but a finite number of special cases. The methodology used is a generalisation of Bravyi and Haah's method of triorthogonal matrices [Phys. Rev. A 86 052329 (2012)], which may be of independent interest. For completeness, we show explicitly that the qudit color codes generalize to gauge color codes, and share the many of the favorable properties of their qubit counterparts.
Qudit stabiliser codes for $\mathbb{Z}_N$ lattice gauge theories with matter
University of Trento（特伦托大学）；INFN-TIFPA Trento Institute of Fundamental Physics and Applications（INFN-TIFPA 特伦托基础物理与应用研究所）；University of Toronto（多伦多大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
Non-Abelian String-Breaking Dynamics on a Qudit Quantum Computer
Universität Innsbruck（因斯布鲁克大学）；Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）；Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学-西班牙国家科学研究委员会理论物理研究所）
Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to $\mathbb{D}_8$
The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；ICREA（加泰罗尼亚高级研究所）；University of Trento（特伦托大学）；INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（INFN-TIFPA，特伦托基础物理与应用研究院）
Institute for Advancing Intelligence, TCG CREST（TCG CREST 推进智能研究所）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学量子信息与计算科学联合中心）
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）
