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An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Insdel errors occur in communication systems caused by the loss of positional information of the message. Since the work by Guruswami and Wang, there have been some further investigations on the list decoding of insertion codes, deletion…
The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…
In the paper titled "Encoding A Qubit In An Oscillator" Gottesman, Kitaev, and Preskill [quant-ph/0008040] described a method to encode a qubit in the continuous Hilbert space of an oscillator's position and momentum variables. This…
Quantum insertion errors are a class of errors that increase the number of qubits in a quantum system. Despite a wealth of research on classical insertion errors, there has been limited progress towards a general framework for correcting…
We propose to use a collective excitation blockade mechanism to identify errors that occur due to disturbances of single atoms in ensemble quantum registers where qubits are stored in the collective population of different internal atomic…
There are two gradient descent decoding procedures for binary codes proposed independently by Liebler and by Ashikhmin and Barg. Liebler in his paper mentions that both algorithms have the same philosophy but in fact they are rather…
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a…
In this work, we introduce a new concatenation scheme which aims at protecting information against the occurrence of both computational errors and quantum erasures. According to our scheme, the internal code must be a quantum…
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…
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…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…
Motivated by the sequence reconstruction problem from traces in DNA-based storage, we consider the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder. We propose simple…
This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known…
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…
In this paper, faulty successive cancellation decoding of polar codes for the binary erasure channel is studied. To this end, a simple erasure-based fault model is introduced to represent errors in the decoder and it is shown that, under…
In this paper, we extend the work of (Abbondati et al., 2024) on decoding simultaneous rational number codes by addressing two important scenarios: multiplicities and the presence of bad primes (divisors of denominators). First, we…
We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum…