Related papers: Reinforcement Learning Enhanced Greedy Decoding fo…

We study the hardness of the problem of finding the distance of quantum error-correcting codes. The analogous problem for classical codes is known to be NP-hard, even in approximate form. For quantum codes, various problems related to…

While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…

We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First,…

There has been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes, using Hermitian self-orthogonal codes, seems to be a difficult problem in general. In this paper,…

The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…

We present SimultaneousGreedys, a deterministic algorithm for constrained submodular maximization. At a high level, the algorithm maintains $\ell$ solutions and greedily updates them in a simultaneous fashion. SimultaneousGreedys achieves…

Quantization is a common approach to mitigate the communication cost of federated learning (FL). In practice, the quantized local parameters are further encoded via an entropy coding technique, such as Huffman coding, for efficient data…

Recent years have witnessed a growing trend toward employing deep reinforcement learning (Deep-RL) to derive heuristics for combinatorial optimization (CO) problems on graphs. Maximum Coverage Problem (MCP) and its probabilistic variant on…

We study the decoding problem for quantum Tanner codes and propose to exploit the underlying local code structure by grouping check nodes into more powerful generalized check nodes for enhanced iterative belief propagation (BP) decoding by…

Large language models solve complex tasks by generating long reasoning chains, achieving higher accuracy at the cost of increased computational cost and reduced ability to isolate functionally relevant reasoning. Prior work on compact…

Reinforcement Learning (RL) has emerged as a powerful framework for sequential decision-making in dynamic environments, particularly when system parameters are unknown. This paper investigates RL-based control for entropy-regularized…

Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for…

We consider an optimization problem where the decision variable is a string of bounded length. For some time there has been an interest in bounding the performance of the greedy strategy for this problem. Here, we provide weakened…

We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms…

Linear reversible circuits represent a subclass of reversible circuits with many applications in quantum computing. These circuits can be efficiently simulated by classical computers and their size is polynomially bounded by the number of…

Fault-tolerant syndrome extraction is a key ingredient in implementing fault-tolerant quantum computations. While conventional methods use a number of extra qubits linear in the weight of the syndrome, several improvements have been…

We analyze the Guruswami--Sudan list decoding algorithm for Reed--Solomon codes over the complex field for sparse recovery in Compressed Sensing. We propose methods of stabilizing both the interpolation and the root-finding steps against…

We introduce a sliding window decoder based on belief propagation (BP) with guided decimation for the purposes of decoding quantum low-density parity-check codes in the presence of circuit-level noise. Windowed decoding keeps the decoding…

We study a comprehensive list of quantum codes as candidates of codes to be used at the bottom, physical, level in a fault-tolerant code architecture. Using the Aliferis-Gottesman-Preskill (AGP) ex-Rec method we calculate the…

Deep linear networks trained with gradient descent yield low rank solutions, as is typically studied in matrix factorization. In this paper, we take a step further and analyze implicit rank regularization in autoencoders. We show greedy…