相关论文: Classical and Quantum algorithms for generic Syndr…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…
Decoded Quantum Interferometry (DQI) is a recently introduced quantum algorithm that reduces discrete optimization to decoding with potential advantages over the best-known polynomial-time classical algorithms for certain Max-LINSAT…
In this paper, the paradigm of sphere decoding (SD) for solving the integer least square problem (ILS) is revisited, where extra degrees of freedom are introduced to exploit the decoding potential. Firstly, the equivalent sphere decoding…
A new protograph-based framework for message passing (MP) decoding of low density parity-check (LDPC) codes with Hamming weight amplifiers (HWAs), which are used e.g. in the NIST post-quantum crypto candidate LEDAcrypt, is proposed. The…
We consider the decoding problem or the problem of finding low weight codewords for rank metric codes. We show how additional information about the codeword we want to find under the form of certain linear combinations of the entries of the…
We design a quantum method for classical information compression that exploits the hidden subgroup quantum algorithm. We consider sequence data in a database with a priori unknown symmetries of the hidden subgroup type. We prove that data…
Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions…
Random classical codes have good error correcting properties, and yet they are notoriously hard to decode in practice. Despite many decades of extensive study, the fastest known algorithms still run in exponential time. The Learning Parity…
Quantum error correction (QEC) with single-shot decoding enables reduction of errors after every single round of noisy stabilizer measurement, easing the time-overhead requirements for fault tolerance. Notably, several classes of quantum…
Fast classical processing is essential for most quantum fault-tolerance architectures. We introduce a sliding-window decoding scheme that provides fast classical processing for the surface code through parallelism. Our scheme divides the…
Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
We consider the quantum decoding problem. It consists in recovering a codeword given a superposition of noisy versions of this codeword. By measuring the superposition, we get back to the classical decoding problem. It appears for the first…
We show a simple reduction which demonstrates the cryptographic hardness of learning a single periodic neuron over isotropic Gaussian distributions in the presence of noise. More precisely, our reduction shows that any polynomial-time…
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as…
In this paper we present quantum information set decoding (ISD) algorithms for binary linear codes. First, we give an alternative view on the quantum walk based algorithms proposed by Kachigar and Tillich (PQCrypto'17). It is more general…
In this paper, we propose a new linear-equation ordered-statistics decoding (LE-OSD). Unlike the OSD, LE-OSD uses high reliable parity bits rather than information bits to recover the codeword estimates, which is equivalent to solving a…
Post-quantum cryptography has gained attention due to the need for secure cryptographic systems in the face of quantum computing. Code-based and lattice-based cryptography are two prominent approaches, both heavily studied within the NIST…
Reed--Solomon error-correcting codes are ubiquitous across computer science and information theory, with applications in cryptography, computational complexity, communication and storage systems, and more. Most works on efficient error…
Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations…