Related papers: Scheme for constructing graphs associated with sta…
Codeword stabilized (CWS) codes are a general class of quantum codes that includes stabilizer codes and many families of non-additive codes with good parameters. For such a non-additive code correcting all t-qubit errors, we propose an…
Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…
The concept of generalized concatenated quantum codes (GCQC) provides a systematic way for constructing good quantum codes from short component codes. We introduce a stabilizer formalism for GCQCs, which is achieved by defining quantum…
A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
Codeword stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and non-additive quantum codes. Standard codeword stabilized quantum codes encode quantum information into…
Improving the simulation of quantum circuits on classical computers is important for understanding quantum advantage and increasing development speed. In this paper, we explore a new way to express stabilizer states and further improve the…
In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes, including additive and nonadditive codes, based on the codeword stabilized framework on subsystems. The codeword stabilized…
We start by studying the subgroup structures underlying stabilizer circuits and we use our results to propose a new normal form for stabilizer circuits. This normal form is computed by induction using simple conjugation rules in the…
Graph states are generalized from qubits to collections of $n$ qudits of arbitrary dimension $D$, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2…
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…
The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the…
A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable…
We present a simple protocol for certifying graph states in quantum networks using stabiliser measurements. The certification statements can easily be applied to different protocols using graph states. We see for example how it can be used…
Given their potential for fault-tolerant operations, topological quantum states are currently the focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer…
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…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
The ubiquity of stabilizer circuits in the design and operation of quantum computers makes techniques to verify their correctness essential. The simulation of stabilizer circuits, which aims to replicate their behavior using a classical…
We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…