相关论文: Lifting a CSS code via its handlebody realization
We propose a notion of lift for quantum CSS codes, inspired by the geometrical construction of Freedman and Hastings. It is based on the existence of a canonical complex associated to any CSS code, that we introduce under the name of Tanner…
We introduce new families of quantum Tanner codes, a class of quantum codes that first appeared in the work of Leverrier and Z\'emor (FOCS 2022). These codes are built from two classical Tanner codes, for which the underlying graphs are…
We generalize the concept of folding from surface codes to CSS codes by considering certain dualities within them. In particular, this gives a general method to implement logical operations in suitable LDPC quantum codes using transversal…
The relation between stabilizer codes and binary codes provided by Gottesman and Calderbank et al. is a celebrated result, as it allows the lifting of classical codes to quantum codes. An equivalent way to state this result is that the work…
Topological quantum codes are favored because they allow qubit layouts that are suitable for practical implementation. An $N$-qubit topological code can be decoded by minimum-weight perfect matching (MWPM) with complexity…
We establish dihedral quantum codes of short block length, a class of CSS codes obtained by the lifted product construction. We present the code construction and give a formula for the code dimension, depending on the two classical codes…
The hypergraph product (HGP) is a famous code construction technique with an equally famous canonical visualisation. This visual perspective provides much more than simply a way to build intuition: HGP codes can be defined graphically,…
We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the…
Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of…
The design of decoding algorithms is a significant technological component in the development of fault-tolerant quantum computers. Often design of quantum decoders is inspired by classical decoding algorithms, but there are no general…
This article presents new constructions of quantum error correcting Calderbank-Shor-Steane (CSS for short) codes. These codes are mainly obtained by Sloane's classical combinations of linear codes applied here to the case of self-orthogonal…
In this article, we define homological quantum codes in arbitrary qudit dimensions $D\geq 2$ by directly defining CSS operators on a 2-Complex $\Sigma$. If the 2-Complex is constructed from a surface, we obtain a qudit surface code. We then…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
Quantum subsystem codes have been shown to improve error-correction performance, ease the implementation of logical operations on codes, and make stabilizer measurements easier by decomposing stabilizers into smaller-weight gauge operators.…
We introduce a framework for implementing logic in CSS quantum error correction codes, building on the surgery methods of Cowtan and Burton [CB24]. Our approach offers a systematic methodology for designing and analysing surgery protocols.…
Large-scale fault-tolerant quantum computation requires compiling logical circuits into physical operations tailored to a given architecture. Prior work addressing this challenge has mostly focused on the surface code and lattice surgery…
The color code model is a crucial instance of a Calderbank--Shor--Steane (CSS)-type topological quantum error-correcting code, which notably supports transversal implementation of the full Clifford group. Its robustness against local noise…
Generating high-quality and diverse human images is an important yet challenging task in vision and graphics. However, existing generative models often fall short under the high diversity of clothing shapes and textures. Furthermore, the…
We develop a topological theory for fault-tolerant quantum computation in quantum low-density parity-check (qLDPC) codes. We show that there exist hidden simplicial or CW complex structures encoding the topological data for all qLDPC and…