Related papers: On the decoding of 1-Fibonacci error correcting co…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
Slow running or straggler tasks can significantly reduce computation speed in distributed computation. Recently, coding-theory-inspired approaches have been applied to mitigate the effect of straggling, through embedding redundancy in…
Recent work by Smagloy et al. (ISIT 2020) shows that the redundancy of a single-deletion $s$-substitution correcting code is asymptotically at least $(s+1)\log n+o(\log n)$, where $n$ is the length of the codes. They also provide a…
Two-dimensional error-correcting codes, where codewords are represented as $n \times n$ arrays over a $q$-ary alphabet, find important applications in areas such as QR codes, DNA-based storage, and racetrack memories. Among the possible…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone…
A major milestone of quantum error correction is to achieve the fault-tolerance threshold beyond which quantum computers can be made arbitrarily accurate. This requires extraordinary resources and engineering efforts. We show that even…
This paper describes design of a low-complexity algorithm for adaptive encoding/ decoding of binary sequences produced by memoryless sources. The algorithm implements universal block codes constructed for a set of contexts identified by the…
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…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
We discuss how the loop calculus approach of [Chertkov, Chernyak '06], enhanced by the pseudo-codeword search algorithm of [Chertkov, Stepanov '06] and the facet-guessing idea from [Dimakis, Wainwright '06], improves decoding of graph based…
Accurate decoding of quantum error-correcting codes is a crucial ingredient in protecting quantum information from decoherence. It requires characterizing the error channels corrupting the logical quantum state and providing this…
We develop novel protocols for generating loss-tolerant quantum codes; these are central for safeguarding information against qubit losses, with most crucial applications in quantum communications. Contrary to current proposals, our method…
One of the founding results of lattice based cryptography is a quantum reduction from the Short Integer Solution problem to the Learning with Errors problem introduced by Regev. It has recently been pointed out by Chen, Liu and Zhandry that…
Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be…
Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…
Coded computation is a method to mitigate "stragglers" in distributed computing systems through the use of error correction coding that has lately received significant attention. First used in vector-matrix multiplication, the range of…