Related papers: Approaching the Quantum Singleton Bound with Appro…
Locally repairable codes (LRC) have recently been a subject of intense research due to theoretical appeal and their application in distributed storage systems. In an LRC, any coordinate of a codeword can be recovered by accessing only few…
Assuming we are in a Word-RAM model with word size $w$, we show that we can construct in $o(w)$ time an error correcting code with a constant relative positive distance that maps numbers of $w$ bits into $\Theta(w)$-bit numbers, and such…
Error-correcting codes are usually envisioned to counter errors by operating unitary corrections depending on the projective measurement results of some syndrome observables. We here propose a way to use them in a more integrated way, where…
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst…
We consider the decoding of linear and array codes from errors when we are only allowed to download a part of the codeword. More specifically, suppose that we have encoded $k$ data symbols using an $(n,k)$ code with code length $n$ and…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
We explore the design of quantum error-correcting codes for cases where the decoherence events of qubits are correlated. In particular, we consider the case where only spatially contiguous qubits decohere, which is analogous to the case of…
We show that any q-ary code with sufficiently good distance can be randomly punctured to obtain, with high probability, a code that is list decodable up to radius $1 - 1/q - \epsilon$ with near-optimal rate and list sizes. Our results imply…
We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…
An algorithm is presented for error correction in the surface code quantum memory. This is shown to correct depolarizing noise up to a threshold error rate of 18.5%, exceeding previous results and coming close to the upper bound of 18.9%.…
I give a pedagogical account of Shor's nine-bit code for correcting arbitrary errors on single qubits, and I review work that determines when it is possible to maintain quantum coherence by reversing the deleterious effects of open-system…
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…
The existence of quantum error correcting codes is one of the most counterintuitive and potentially technologically important discoveries of quantum information theory. However, standard error correction refers to abstract quantum…
A minimal depth quantum circuit implementing 5-qubit quantum error correction in a manner optimized for a linear nearest neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that…
Motivated by limitations and capabilities of neutral atom qubits, we examine whether measurement-free error correction can produce practical error thresholds. We show that this can be achieved by extracting redundant syndrome information,…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Linear codes correcting one deletions have rate at most $1/2$. In this paper, we construct linear list decodable codes correcting edits with rate approaching $1$ and reasonable list size. Our encoder and decoder run in polynomial time.
It is not so well-known that measurement-free quantum error correction protocols can be designed to achieve fault-tolerant quantum computing. Despite the potential advantages of using such protocols in terms of the relaxation of accuracy,…