We construct surface codes corresponding to genus greater than one in the context of quantum error correction. The architecture is inspired by the topology of invariant integral surfaces of certain non-integrable classical billiards. Corresponding to the fundamental domains of rhombus and square torus billiard, surface codes of genus two and five are presented here. There is significant improvement in encoding rates and code distance, in addition to immunity against noise.
The toric code is a simple and exactly solvable example of topological order realising Abelian anyons. However, it was shown to support non-local lattice defects, namely twists, which exhibit non-Abelian anyonic behaviour [1]. Motivated by this result, we investigated the potential of having non-Abelian statistics from puncture defects on the toric code. We demonstrate that an encoding with mixed-boundary punctures reproduces Ising fusion, and a logical Pauli-$X$ upon their braiding. Our construction paves the way for local lattice defects to exhibit non-Abelian properties that can be employed…
The surface code is a leading candidate quantum error correcting code, owing to its high threshold, and compatibility with existing experimental architectures. Bravyi et al. (2006) showed that encoding a state in the surface code using local unitary operations requires time at least linear in the lattice size $L$, however the most efficient known method for encoding an unknown state, introduced by Dennis et al. (2002), has $O(L^2)$ time complexity. Here, we present an optimal local unitary encoding circuit for the planar surface code that uses exactly $2L$ time steps to encode an unknown state…
Higher Nishimori Criticality and Exact Results at the Learning Transition of Deformed Toric Codes
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；University of Cologne（科隆大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Learning Potts Models and $Z_3$ Toric Codes: Higher and Ordinary Nishimori Criticality
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；University of Cologne（科隆大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Disorder-induced quantum Fisher information in topological quantum systems
BITS Pilani KK Birla Goa Campus（比拉戈亚校园）；Harish-Chandra Research Institute（哈里什-昌德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Università di Trento（特伦托大学）；INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（意大利国家核物理研究所-基础物理与应用特伦托研究所）
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or states in a modular fashion. Using a set of local moves known as operator pushing, one can derive properties of the more complex codes, such as transversal non-Clifford gates, by tracing the flow of operators in the network. The framework endows a network geometry to any code it builds and is valid…
Simons Institute for the Theory of Computing, University of California at Berkeley（加州大学伯克利分校西蒙斯理论计算研究所）；ETH Zürich（苏黎世联邦理工学院）；University of California at Berkeley（加州大学伯克利分校）
