Related papers: General Construction of Quantum Error-Correcting C…
Quantum error correction plays a prominent role in the realization of quantum computation, and quantum low-density parity-check (qLDPC) codes are believed to be practically useful stabilizer codes. While qLDPC codes are defined to have…
We study stabilizer quantum error correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension. Building upon 1) a general formula relating the error-susceptibility of a…
This work develops a geometric framework for constructing quantum error-correcting codes from weighted projective and orbifold structures, integrating algebraic geometry, divisor theory, and the CSS stabilizer formalism. Beginning with…
The construction of quantum error-correcting codes (QECCs) with good parameters is a hot topic in the area of quantum information and quantum computing. Quantum maximum distance separable (QMDS) codes are optimal because the minimum…
In this paper, necessary and sufficient conditions for the self-orthogonality of t-generator quasi-cyclic (QC) codes are presented under the Euclidean, Hermitian, and symplectic inner products, respectively. Particularly, by studying the…
Quantum error-correcting code (QECC) is the central ingredient in fault-tolerant quantum information processing. An emerging paradigm of dynamical QECC shows that one can robustly encode logical quantum information both temporally and…
We study a three-fold variant of the hypergraph product code construction, differing from the standard homological product of three classical codes. When instantiated with 3 classical LDPC codes, this "XYZ product" yields a non CSS quantum…
Quantum error correction/detection (QEC/QED) and dynamical decoupling (DD) are tools for protecting quantum information. A natural goal is to combine them to outperform either approach alone. Such a benefit is not automatic: physical DD can…
Among various classes of quantum error correcting codes (QECCs), non-stabilizer codes have rich properties and are of theoretical and practical interest. Decoding non-stabilizer codes is, however, a highly non-trivial task. In this paper,…
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…
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…
We continue the study of classical and quantum low-density parity check (LDPC) codes from a physical perspective. We focus on constructive approaches and formulate a general framework for systematically constructing codes with various…
In a gauge theory, a collection of kinematical degrees of freedom is used to redundantly describe a smaller amount of gauge-invariant information. In a quantum error correcting code (QECC), a collection of computational degrees of freedom…
Is gauge symmetry merely a redundancy in our description, or does it carry a deeper information-theoretic significance? Quantum error-correcting codes (QECCs) show that redundancy can serve as a resource for protecting information against…
The recently introduced Quantum Lego framework provides a powerful method for generating complex quantum error correcting codes (QECCs) out of simple ones. We gamify this process and unlock a new avenue for code design and discovery using…
Single-shot error correction outperforms conventional approaches by requiring only one round of stabilizer measurements for decoding, even in the presence of measurement errors. This capability relates to the confinement property of codes,…
Product constructions constitute a powerful method for generating quantum CSS codes, yielding celebrated examples such as toric codes and asymptotically good low-density parity check (LDPC) codes. Since a CSS code is fully described by a…
Hypergraph products are quantum low-density parity-check (LDPC) codes constructed from two classical LDPC codes. Although their dimension and distance depend only on the parameters of the underlying classical codes, optimizing their…
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…