Related papers: Beyond Integral-Domain Stabilizer Codes
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
One of the most promising paths towards large scale fault tolerant quantum computation is the use of quantum error correcting stabilizer codes. Just like every other quantum circuit, these codes must be compiled to hardware in a way to…
Using nuclear magnetic resonance techniques, we experimentally investigated the effects of applying a two bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without…
Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information storage and transmission. We report the implementation of a concatenated quantum error-correcting code able to correct…
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and…
We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert state space of rotational states of a rigid body. These codes, which protect against both drift in the body's…
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…
The scheme of entanglement-assisted quantum error-correcting (EAQEC) codes assumes that the ebits of the receiver are error-free. In practical situations, errors on these ebits are unavoidable, which diminishes the error-correcting ability…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
We study the performance of quantum error correction codes (QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the…
Quantum replacer codes are codes that can be protected from errors induced by a given set of quantum replacer channels, an important class of quantum channels that includes the erasures of subsets of qubits that arise in quantum error…
Continuous-variable systems protected by bosonic quantum error-correcting codes have emerged as a promising platform for quantum information processing. To date, design of codewords has centered on optimizing the occupation of basis states…
The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either…
One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…
Quasi-twisted codes are used here as the classical ingredients in the so-called Construction X for quantum error-control codes. The construction utilizes nearly self-orthogonal codes to design quantum stabilizer codes. We expand the choices…
Construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
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 article surveys quantum error control, focusing on quantum stabilizer codes, stressing on the how to use classical codes to design good quantum codes. It is to appear as a book chapter in "A Concise Encyclopedia of Coding Theory,"…
We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the…