Related papers: Insertion Correcting Capability for Quantum Deleti…
The error correcting capabilities of the Calderbank-Shor-Steane [[7,1,3]] quantum code, together with a fault-tolerant syndrome extraction by means of several ancilla states, have been numerically studied. A simple probability expression to…
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…
Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such…
We provide a self-contained introduction for entanglement-assisted quantum error-correcting codes in this book chapter.
A general theory of quantum error avoiding codes is established, and new light is shed on the relation between quantum error avoiding and correcting codes. Quantum error avoiding codes are found to be a special type of highly degenerate…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
We show how procedures which can correct phase and amplitude errors can be directly applied to correct errors due to quantum entanglement. We specify general criteria for quantum error correction, introduce quantum versions of the Hamming…
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 most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
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…
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations…
Topological quantum field theories (TQFT) encode quantum correlations in topological features of spaces. In this work, we leverage this feature to explore how information encoded in TQFTs can be stored and retrieved in the presence of local…
The concept of quantum interleaver and a simple method of quantum burst-error correction is proposed. By using the quantum interleaver, any quantum burst-errors that have occurred spread over the interleaved code word, so that we can…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
In coding theory, handling errors that occur when symbols are inserted or deleted from a transmitted message is a long-standing challenge. Optimising redundancy for insertion and deletion channels remains a key open problem with significant…
Quantum error correcting code is a useful tool to combat noise in quantum computation. It is also an important ingredient in a number of unconditionally secure quantum key distribution schemes. Here, I am going to show that quantum code can…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…
Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome.…