Related papers: A Construction of Quantum Codes via A Class of Cla…
We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is con- structed via the tensor product of parity check matrices of the two…
Quantum error correction is one of the fundamental building blocks of digital quantum computation. The Quantum Lego formalism has introduced a systematic way of constructing new stabilizer codes out of basic lego-like building blocks, which…
Let $R=\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ be a non-chain finite commutative ring, where $u^3=u$. In this paper, we mainly study the construction of quantum codes from cyclic codes over $R$. We obtained self-orthogonal codes over…
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…
In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic…
Free categorical constructions characterise quantum computing as the combination of two copies of a reversible classical model, glued by the complementarity equations of classical structures. This recipe effectively constructs a…
Polynomial remainder codes are a large class of codes derived from the Chinese remainder theorem that includes Reed-Solomon codes as a special case. In this paper, we revisit these codes and study them more carefully than in previous work.…
We construct new polar coding schemes for the transmission of quantum or private classical information over arbitrary quantum channels. In the former case, our coding scheme achieves the symmetric coherent information and in the latter the…
Quantum computers theoretically are able to solve certain problems more quickly than any deterministic or probabilistic computers. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, one has to…
We generalize a construction of non-binary quantum LDPC codes over $\F_{2^m}$ due to \cite{KHIS11a} and apply it in particular to toric codes. We obtain in this way not only codes with better rates than toric codes but also improve…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
The extraction of classical degrees of freedom in quantum mechanics is studied in the stochastic variational method. By using this classicalization, a hybrid model constructed from quantum and classical variables (quantum-classical hybrids)…
Construction of good quantum codes via classical codes is an important task for quantum information and quantum computing. In this work, by virtue of a decomposition of the defining set of constacyclic codes we have constructed eight new…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss…
Let $\X$ be an algebraic curve of genus $g \geq 2$ defined over a field $\F_q$ of characteristic $p > 0$. From $\X$, under certain conditions, we can construct an algebraic geometry code $C$. If the code $C$ is self-orthogonal under the…
A simple construction of quaternary hermitian self-orthogonal codes with parameters $[2n+1,k+1]$ and $[2n+2,k+2]$ from a given pair of self-orthogonal $[n,k]$ codes, and its link to quantum codes is considered. As an application, an optimal…
This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
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)…