Related papers: Non-Pauli Observables for CWS Codes
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
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 degeneracy in error correction is a feature unique to quantum error correcting codes, unlike their classical counterpart. It allows a quantum error correcting code to correct errors even when they can not uniquely pinpoint the…
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)…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure, we get codes with good parameters and a code whose parameters exceed the CSS quantum…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
We study translationally invariant Pauli stabilizer codes with qudits of arbitrary, not necessarily uniform, dimensions. Using homological methods, we define a series of invariants called charge modules. We describe their properties and…
In this work we develop a general tensor network decoder for 2D codes. Specifically, we propose a decoder that approximates maximally likelihood decoding for 2D stabiliser and subsystem codes subject to Pauli noise. For a code consisting 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 $\mathcal{C}$, $\mathcal{D}$…
Quantum error correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous…
We apply the quantum error detection scheme Pauli check sandwiching (PCS) to quantum networks by turning it into a distributed multiparty protocol. PCS provides protection on the targeted qubits and generally requires less resource overhead…
Clifford codes are a class of quantum error control codes that form a natural generalization of stabilizer codes. These codes were introduced in 1996 by Knill, but only a single Clifford code was known, which is not already a stabilizer…
We solve the problem of the classification of perfect quantum codes. We prove that the only nontrivial perfect quantum codes are those with the parameters . There exist no other nontrivial perfect quantum codes.
Real quantum computers will be subject to complicated, qubit-dependent noise, instead of simple noise such as depolarizing noise with the same strength for all qubits. We can do quantum error correction more effectively if our decoding…
Quantum error correcting codes (QECCs) in quantum communi- cation systems has been known to exhibit improved performance with the use of error-free entanglement bits (ebits). In practical situations, ebits inevitably suffer from errors, and…
We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms…
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…
CP-PAW is a combined electronic structure and ab-initio molecular dynamics code to perform mixed quantum and classical simulations of atomistic condensed phase systems, such as solids, liquids, and molecular systems. As the name suggests,…