Related papers: Decryption Through Polynomial Ambiguity: Noise-Enh…
Constrained sequence codes have been widely used in modern communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel, hence enabling efficient and reliable…
Polynomial based approaches, such as the Mat-Dot and entangled polynomial codes (EPC) have been used extensively within coded matrix computations to obtain schemes with good recovery thresholds. However, these schemes are well-recognized to…
Another threat is the development of large quantum computers, which have a high likelihood of breaking the high popular security protocols because it can use both Shor and Grover algorithms. In order to fix this looming threat,…
Computationally hard problems based on coding theory, such as the syndrome decoding problem, have been used for constructing secure cryptographic schemes for a long time. Schemes based on these problems are also assumed to be secure against…
Hashing-based methods seek compact and efficient binary codes that preserve the neighborhood structure in the original data space. For most existing hashing methods, an image is first encoded as a vector of hand-crafted visual feature,…
Discrete diffusion models are a powerful, emerging paradigm for code generation. They construct programs through iterative refinement of partially corrupted token sequences and enable parallel token refinement. Importantly, this paradigm…
Deep learning is widely used to uncover hidden patterns in large code corpora. To achieve this, constructing a format that captures the relevant characteristics and features of source code is essential. Graph-based representations have…
We construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel. For Pauli and erasure channels we also present…
Currently there is an active Post-Quantum Cryptography (PQC) solutions search, which attempts to find cryptographic protocols resistant to attacks by means of for instance Shor polynomial time algorithm for numerical field problems like…
Low-frequency noise can induce serious decoherence in superconducting qubits. Due to its diverse physical origin, such noise can couple with the qubits either as transverse or as longitudinal noise. Here, we present a universal quantum…
The polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times. As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method…
Steganography embeds secret messages in seemingly innocuous carriers for covert communication under surveillance. Current Provably Secure Steganography (PSS) schemes based on language models can guarantee computational indistinguishability…
Guessing Random Additive Noise Decoding (GRAND) is a family of hard- and soft-detection error correction decoding algorithms that provide accurate decoding of any moderate redundancy code of any length. Here we establish a method through…
Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. Suchara et al. proposed a framework based on hypergraphs for construction of such codes. They also studied the performance of some…
We construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-qubit measurements in any basis. Our results apply to…
A new approach to quantum cryptography to be called KCQ, keyed communication in quantum noise, is developed on the basis of quantum detection and communication theory for classical information transmission. By the use of a shared secret key…
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…
To ensure that text generated by large language models (LLMs) is in an expected format, constrained decoding proposes to enforce strict formal language constraints during generation. However, as we show in this work, not only do such…
We propose an interpretable graph neural network framework to denoise single or multiple noisy graph signals. The proposed graph unrolling networks expand algorithm unrolling to the graph domain and provide an interpretation of the…
We provide a complete proof of the security of quantum cryptography against any eavesdropping attack including coherent measurements even in the presence of noise. Polarization-based cryptographic schemes are shown to be equivalent to…