Related papers: Good binary quantum codes with transversal CCZ gat…
Quasi-twisted (QT) codes are a generalization of quasi-cyclic (QC) codes. Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented. It is also shown that…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good…
This work classifies stabilizer codes by the set of diagonal Clifford gates that can be implemented transversally on them. We show that, for any stabilizer code, its group of diagonal transversal Clifford gates on $\ell$ code blocks must be…
In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…
In this paper we investigate the use of quantum information to share classical secrets. While every quantum secret sharing scheme is a quantum error correcting code, the converse is not true. Motivated by this we sought to find quantum…
Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the…
Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation…
The spin states of single electrons in gate-defined quantum dots satisfy crucial requirements for a practical quantum computer. These include extremely long coherence times, high-fidelity quantum operation, and the ability to shuttle…
In this paper, we investigate the transversality of pairs of CSS codes and their use in the second generation of quantum repeaters (QR)s. We show that different stations of quantum link can experience different errors. Considering this…
A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but subclasses have been studied previously by other authors. The algebras are indexed by double partitions or double flag varieties.…
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…
Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal…
Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are {\em transversal}, acting bitwise…
Quantum low-density parity-check codes are promising candidates towards scalable fault-tolerant quantum computation. Among these, bivariate bicycle (BB) codes offer superior encoding rates and large code distance compared to surface codes.…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…
We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product,…
Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important role in coding theory. In this paper, we study some results on GQC codes over $\mathbb{Z}_4$ including the normalized generating…
In this paper, we present a new construction of asymmetric quantum codes (AQCs) by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs)…