Related papers: An algebraic characterization of binary CSS-T code…
We characterize novel probability distributions for CSS codes. Such classes of error correcting codes, originally introduced by Calderbank, Shor, and Steane, are of great significance in advancing the fidelity of Quantum computation, with…
A Z2-triple cyclic code of block length (r,s,t) is a binary code of length r+s+t such that the code is partitioned into three parts of lengthsr,s andt such that each of the three parts is invariant under the cyclic shifts of the…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be…
In our recent paper entitled "Quantum Quasi-Cyclic Low-Density Parity-Check codes" [ICIC 2009. LNCS 5754], it was claimed that some new quantum codes can be constructed via the CSS encoding/decoding approach with various lengths and rates.…
Magic states are fundamental building blocks on the road to fault-tolerant quantum computing. CSS codes play a crucial role in the construction of magic distillation protocols. Previous work has cast quantum computing with magic states for…
Collective coherent (CC) errors are inevitable, as every physical qubit undergoes free evolution under its kinetic Hamiltonian. These errors can be more damaging than stochastic Pauli errors because they affect all qubits coherently,…
We characterize the affine-invariant maximal extended cyclic codes. Then by the CSS construction, we derive from these codes a family of pure quantum codes. Also for ordnq even, a new family of degenerate quantum stabilizer codes is derived…
Two-dimensional topological translationally-invariant (TTI) quantum codes, such as the toric code (TC) and bivariate bicycle (BB) codes, are promising candidates for fault-tolerant quantum computation. For such codes to be practically…
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…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and…
Building scalable quantum computers requires quantum error-correcting codes that enable reliable operations in the presence of noise. Motivated by such need, this paper introduces two constructions of high-rate, quantum dual-containing (DC)…
Recently, binary cyclic codes with parameters $[n,(n\pm1)/2,\geq \sqrt{n}]$ have been a hot topic since their minimum distances have a square-root bound. In this paper, we construct four classes of binary cyclic codes…
In this paper we estimate the fidelity of stabilizer and CSS codes. First, we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator. Next, we find the average quantum enumerators of the ensembles of finite…
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…
Linear complementary dual (LCD) cyclic codes were referred historically to as reversible cyclic codes, which had applications in data storage. Due to a newly discovered application in cryptography, there has been renewed interest in LCD…
BCH and LCD cyclic codes of length $n=\lambda(q^m+1)$ with $\lambda\mid q-1$ are studied. A complete characterization of $q$-cyclotomic cosets modulo $n$ is given: Theorem \ref{th4} provides a necessary and sufficient condition for any…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…