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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…
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…
Sequential decoding, commonly applied to substitution channels, is a sub-optimal alternative to Viterbi decoding with significantly reduced memory costs. In this work, a sequential decoder for convolutional codes over channels that are…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
When data is stored, compressed, or communicated through a media such as cable or air, sources of noise and other parameters such as EMI, crosstalk, and distance can considerably affect the reliability of these data. Error detection and…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
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…
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…
This paper considers rateless network error correction codes for reliable multicast in the presence of adversarial errors. Most existing network error correction codes are designed for a given network capacity and maximum number of errors…
Communication-avoiding algorithms allow redundant computations to minimize the number of inter-process communications. In this paper, we propose to exploit this redundancy for fault-tolerance purpose. We illustrate this idea with QR…
In the shallow sub-threshold regime, fault-tolerant quantum computation requires a tremendous amount of qubits. In this paper, we study the error correction in the deep sub-threshold regime. We estimate the physical error rate for achieving…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…
Quantum error correction (QEC) will be essential to achieve the accuracy needed for quantum computers to realise their full potential. The field has seen promising progress with demonstrations of early QEC and real-time decoded experiments.…
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
Decoherence is the main problem to be solved before quantum computers can be built. To control decoherence, it is possible to use error correction methods, but these methods are themselves noisy quantum computation processes. In this work…
In this paper, we present a new family of fountain codes which overcome adversarial errors. That is, we consider the possibility that some portion of the arriving packets of a rateless erasure code are corrupted in an undetectable fashion.…
Fracton topological phases have a large number of materialized symmetries that enforce a rigid structure on their excitations. Remarkably, we find that the symmetries of a quantum error-correcting code based on a fracton phase enable us to…