We give a new algorithm for computing the robustness of magic - a measure of the utility of quantum states as a computational resource. Our work is motivated by the magic state model of fault-tolerant quantum computation. In this model, all unitaries belong to the Clifford group. Non-Clifford operations are effected by injecting non-stabiliser states, which are referred to as magic states in this context. The robustness of magic measures the complexity of simulating such a circuit using a classical Monte Carlo algorithm. It is closely related to the degree negativity that slows down Monte Carlo simulations through the infamous sign problem. Surprisingly, the robustness of magic is submultiplicative. This implies that the classical simulation overhead scales subexponentially with the number of injected magic states - better than a naive analysis would suggest. However, determining the robustness of n copies of a magic state is difficult, as its definition involves a convex optimisation problem in a 4^n-dimensional space. In this paper, we make use of inherent symmetries to reduce the problem to n dimensions. The total run-time of our algorithm, while still exponential in n, is super-polynomially faster than previously published methods. We provide a computer implementation and give the robustness of up to 10 copies of the most commonly used magic states. Guided by the exact results, we find a finite hierarchy of approximate solutions where each level can be evaluated in polynomial time and yields rigorous upper bounds to the robustness. Technically, we use symmetries of the stabiliser polytope to connect the robustness of magic to the geometry of a low-dimensional convex polytope generated by certain signed quantum weight enumerators. As a by-product, we characterised the automorphism group of the stabiliser polytope, and, more generally, of projections onto complex projective 3-designs.
Simulation of quantum computation with magic states via Jordan-Wigner transformations
University of British Columbia（不列颠哥伦比亚大学）；Stewart Blusson Quantum Matter Institute, University of British Columbia（不列颠哥伦比亚大学斯图尔特·布拉斯量子物质研究所）；Simon Fraser University（西蒙菲莎大学）；University of Sydney（悉尼大学）；Leibniz University Hannover（汉诺威莱布尼茨大学）
Institute of Theoretical Physics, University of Wrocław（弗罗茨瓦夫大学理论物理研究所）；Institute of Theoretical Physics, Faculty of Physics, University of Warsaw（华沙大学物理学院理论物理研究所）
Generative AI Beyond Tokens: Quantum Resource Consumption of IQP Circuits
Technical University of Applied Sciences Regensburg（雷根斯堡应用技术大学）；Universität der Bundeswehr München（联邦国防军慕尼黑大学）；Siemens AG, Foundational Technology（西门子股份公司基础技术部门）
Federal University of Rio Grande do Norte（北里奥格兰德联邦大学）；International Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）；Center for Macroscopic Quantum States bigQ, Department of Physics, Technical University of Denmark（丹麦技术大学宏观量子态中心bigQ）
Graph Theoretic Approach to Quantum Nonstabilizerness
Instituut-Lorentz, Universiteit Leiden（莱顿大学洛伦兹研究所）；Applied Quantum Algorithms, Leiden University（莱顿大学应用量子算法）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；The Hong Kong University of Science and Technology（香港科技大学）；Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova（帕多瓦大学伽利略物理与天文系）；Padua Quantum Technologies Research Center, Università degli Studi di Padova（帕多瓦大学帕多瓦量子技术研究中心）
Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
Tencent Quantum Laboratory（腾讯量子实验室）；HUN-REN Alfréd Rényi Institute of Mathematics（匈牙利冯·诺依曼数学研究所）；HUN-REN Institute for Computer Science and Control（匈牙利计算机科学与控制研究所）；Centre for Quantum Technologies（量子技术中心）；National University of Singapore（新加坡国立大学）；CNRS, IRIF, Université Paris Cité（法国国家科学研究中心、IRIF、巴黎Cité大学）
Quantum contextual finite geometries from dessins d'enfants
我们指出了一个明确的连接图绘制在紧凑的黎曼曲面上定义的领域$\bar{\mathbb{Q}}$的代数数-所谓的Grothendieck的{ \it dessins d 'enfants} -和丰富的杰出的点线配置。这些包括单纯形，交叉多面体，几个显着的射影配置，一些多部图和一些“异国情调”的几何形状。值得注意的是，我们不仅发现了Mermin幻方和幻方五角星的基础，而且发现了与两量子位和三量子位泡利群几何相关的基础。特别有趣的是所有三种类型的细长广义四边形，即GQ（2，1），GQ（2，2）和GQ（2，4），以及一对密切相关的图，即Schläfli和Clebsch图的出现。这些发现似乎表明，{ \it dessins d 'enfants}可能会为我们提供一个新的强大的工具，以获得更深入的了解有限维希尔伯特空间及其相关群体的性质，特别强调上下文。
