Related papers: Entanglement-Assisted Quantum Error-Correcting Cod…
By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality…
The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
From the set of operators for errors and its correction code, we introduce the so-called complete unitary transformation. It can be used for encoding while the inverse of it can be applied for correcting the errors of the encoded qubit. We…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is the code resulting from exchanging the original code's information qubits with its ebits. To introduce this notion, we show how entanglement-assisted (EA)…
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,"…
This paper proves that any quantum t-deletion-correcting codes also correct a total of t insertion and deletion errors under a certain condition. Here, this condition is that a set of quantum states is defined as a quantum error-correcting…
We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context…
The key realisation which lead to the emergence of the new field of quantum information processing is that quantum mechanics, the theory that describes microscopic particles, allows the processing of information in fundamentally new ways.…
In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial…
We transfer the concept of linear feed-back shift registers to quantum circuits. It is shown how to use these quantum linear shift registers for encoding and decoding cyclic quantum error-correcting codes.
Error correction, in the standard meaning of the term, implies the ability to correct all small analog errors and some large errors. Examining assumptions at the basis of the recently proposed quantum error-correcting codes, it is pointed…
We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted…
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is defined from the orthogonal group of a simplified stabilizer group. From the Poisson summation formula, this duality leads to the MacWilliams identities and…
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by…
In this contribution we will give a brief overview on the methods used to overcome decoherence in quantum communication protocols. We give an introduction to quantum error correction, entanglement purification and quantum cryptography. It…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…
The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of…
Active quantum error correction is a central ingredient to achieve robust quantum processors. In this paper we investigate the potential of quantum machine learning for quantum error correction in a quantum memory. Specifically, we…