Related papers: Quantum Reduction of Finding Short Code Vectors to…
In this paper we study the hardness of the syndrome decoding problem over finite rings endowed with the Lee metric. We first prove that the decisional version of the problem is NP-complete, by a reduction from the $3$-dimensional matching…
We provide a new approach to error mitigation for quantum chemistry simulation that uses a Bravyi-Kitaev Superfast encoding to implement a quantum error detecting code within the fermionic encoding. Our construction has low-weight parity…
This paper presents an algorithm for decoding homogeneous interleaved codes of high interleaving order in the rank metric. The new decoder is an adaption of the Hamming-metric decoder by Metzner and Kapturowski (1990) and guarantees to…
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…
We present an efficient quantum algorithm for a structured state discrimination problem we call the subspace decoding task. Building on this, we show that the algorithm enables efficient and optimal decoding of certain families of…
Weighted Hamming distance, as a similarity measure between binary codes and binary queries, provides superior accuracy in search tasks than Hamming distance. However, how to efficiently and accurately find $K$ binary codes that have the…
Determining the largest size, or equivalently finding the lowest redundancy, of q-ary codes for given length and minimum distance is one of the central and fundamental problems in coding theory. Inspired by the construction of…
We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated…
We design the first efficient algorithms and prove new combinatorial bounds for list decoding tensor products of codes and interleaved codes. We show that for {\em every} code, the ratio of its list decoding radius to its minimum distance…
Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer,…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
The aim of this paper is to provide a quantum counterpart of the well known minimum-distance classifier named Nearest Mean Classifier (NMC). In particular, we refer to the following previous works: i) in Sergioli et al. 2016, we have…
We propose an algorithm using the Gaussian elimination method to find the minimal Hamming distance and decode received messages of linear codes. This algorithm is easy to implement as it requires no Gr\"obner bases to compute solutions for…
We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight…
This paper introduces a new counting code. Its design was motivated by distributed video coding where, for decoding, error correction methods are applied to improve predictions. Those error corrections sometimes fail which results in…
The syndrome decoding problem has been proposed as a computational hardness assumption for code based cryptosystem that are safe against quantum computing. The problem has been reduced to finding the codeword with the smallest non-zero…
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code…
Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…
Linear programming approaches have been applied to derive upper bounds on the size of classical codes and quantum codes. In this paper, we derive similar results for general quantum codes with entanglement assistance, including nonadditive…
Locally Decodable Codes (LDCs) are error-correcting codes $C\colon\Sigma^n\rightarrow \Sigma^m,$ encoding \emph{messages} in $\Sigma^n$ to \emph{codewords} in $\Sigma^m$, with super-fast decoding algorithms. They are important mathematical…