Related papers: A Class of Cyclic Quantum Codes
Is the notion of a quantum computer resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting quantum computers. To this end, we…
Surface codes are one of the most important topological stabilizer codes in the theory of quantum error correction. In this paper, we provide an efficient way to obtain surface codes through Measurement-based quantum computation (MBQC)…
Fault-tolerant cluster states form the basis for scalable measurement-based quantum computation. Recently, new stabilizer codes for scalable circuit-based quantum computation have been introduced that have very high thresholds under biased…
We show that concrete hardness assumptions about learning or cloning the output state of a random quantum circuit can be used as the foundation for secure quantum cryptography. In particular, under these assumptions we construct secure…
The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The…
We first present a useful characterization of additive (stabilizer) quantum error-correcting codes. Then we present several examples of We first present a useful characterization of additive (stabilizer) quantum error--correcting codes.…
Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimisation and execution of the expressed computations. However,…
The Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation. However, direct methods to increase its logical dimensions, such as lattice surgery or introducing…
In addition to their applications in data storage, communications systems, and consumer electronics, LCD codes -- a class of linear codes -- have been employed in cryptography recently. LCD cyclic codes were referred to as reversible cyclic…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we…
Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find its analogue in quantum information field, which are called quantum polar codes. However, no one has…
In this paper, we give a constructive proof to show that if there exist a classical linear code C is a subset of F_q^n of dimension k and a classical linear code D is a subset of F_q^k^m of dimension s, where q is a power of a prime number…
Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on…
We develop genetic algorithms for searching quantum circuits, in particular stabilizer quantum error correction codes. Quantum codes equivalent to notable examples such as the 5-qubit perfect code, Shor's code, and the 7-qubit color code…
Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. With the aid of the largest subfield over which the given…
We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can…
Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is--paradoxically--itself prone to errors. Decoherence free subspaces, on the other hand,…
Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes $\mathcal{C}$, $\mathcal{D}$…