Related papers: Subsystem CSS codes, a tighter stabilizer-to-CSS m…
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
We present an algorithm that takes a CSS stabilizer code as input, and outputs another CSS stabilizer code such that the stabilizer generators all have weights $O(1)$ and such that $O(1)$ generators act on any given qubit. The number of…
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 study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum…
The two-dimensional color code is an alternative to the toric code that encodes more logical qubits while maintaining crucial features of the $\mathbb{Z}_2\times\mathbb{Z}_2$ toric code in the long wavelength limit. However its short range…
We characterize the structure of 2-quasi-cyclic codes over a finite field F by the so-called Goursat Lemma. With the characterization, we exhibit a necessary and sufficient condition for a 2-quasi-cyclic code being a dihedral code. And we…
The Measurement-based quantum computation provides an alternate model for quantum computation compared to the well-known gate-based model. It uses qubits prepared in a specific entangled state followed by single-qubit measurements. The…
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…
Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. For quantum codes, a form of puncturing is known, but its description is based on the code space rather than its…
The geometric measure, the logarithmic robustness and the relative entropy of entanglement are proved to be equal for a stabilizer quantum codeword. The entanglement upper and lower bounds are determined with the generators of code. The…
Simulation of stabilizer circuits is a well-studied problem in quantum information processing, with a number of highly optimized algorithms available. Yet, we argue that further improvements can arise from the theoretical structure of…
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 $\mathcal{C}$, $\mathcal{D}$…
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes $(C_1, C_2)$ such that $C_1$ contains $C_2$, $C_2$ is even, and…
We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph…
Graphs and recently hypergraphs have been known as an important tool for considering different properties of quantum many-body systems. In this paper, we study a mapping between an important class of quantum systems namely quantum…
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…
In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. We concatenate alternant codes with any linear code achieving…
The codeword stabilized (CWS) quantum codes formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes (arXiv:0708.1021 [quant-ph]), but only for binary states. Here we generalize the CWS…
We introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes. We apply this framework to bosonic coding, obtaining multimode extensions of the cat…
We propose a systematic procedure for the construction of graphs associated with binary quantum stabilizer codes. The procedure is characterized by means of the following three step process. First, the stabilizer code is realized as a…