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Fault-tolerant quantum computers will depend crucially on the performance of the classical decoding algorithm which takes in the results of measurements and outputs corrections to the errors inferred to have occurred. Machine learning…
Finding optimal message quantization is a key requirement for low complexity belief propagation (BP) decoding. To this end, we propose a floating-point surrogate model that imitates quantization effects as additions of uniform noise, whose…
Quantum low-density parity-check (qLDPC) codes are quantum stabilizer codes where each stabilizer acts on a constant number of qubits and each qubit is acted on by a constant number of stabilizers. We study qLDPC codes constructed from…
In this paper, we propose a new decoder, called the Multiple-Bases Belief-Propagation List Decoder (MBBP-LD), for Quantum Low-Density Parity-Check (QLDPC) codes. It extends the Multiple-Bases Belief-Propagation (MBBP) framework, originally…
We address noisy message-passing decoding of lowdensity parity-check (LDPC) codes over additive white Gaussian noise channels. Message-passing decoders in which certain processing units iteratively exchange messages are common for decoding…
We present Astra, a novel and scalable decoder using graph neural networks. Our decoder works similarly to solving a Sudoku puzzle of constraints represented by the Tanner graph. In general, Quantum Low Density Parity Check (QLDPC) decoding…
In this work, we explore a new approach to designing both algorithms and error detection codes for preparing approximate ground states of molecules. We propose a classical algorithm to find the optimal stabilizer state by using excitations…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
Simulation of stabilizer circuits is a well-studied problem in quantum information processing, with a number of highly optimized algorithms available. Yet, we argue that further improvements can arise from the theoretical structure of…
In this paper, a new method for decoding Low Density Parity Check (LDPC) codes, based on Multi-Layer Perceptron (MLP) neural networks is proposed. Due to the fact that in neural networks all procedures are processed in parallel, this method…
This letter introduces a novel algorithm for generating codebooks in molecular communications (MC). The proposed algorithm utilizes character entropy to effectively mitigate inter-symbol interference (ISI) during MC via diffusion. Based on…
Many modern imaging applications can be modeled as compressed sensing linear inverse problems. When the measurement operator involved in the inverse problem is sufficiently random, denoising Scalable Message Passing (SMP) algorithms have a…
Dense coding with non-maximally entangled states has been investigated in many different scenarios. We revisit this problem for protocols adopting the standard encoding scheme. In this case, the set of possible classical messages cannot be…
A quantum stabilizer code over GF$(q)$ corresponds to a classical additive code over GF$(q^2)$ that is self-orthogonal with respect to a symplectic inner product. We study the decoding of quantum low-density parity-check (LDPC) codes over…
Poset metrics in the context of stabilizer codes are investigated. MDS stabilizer poset codes are defined. Various characterizations of these quantum codes are found. Methods for producing examples are proposed.
We propose the use of certain low-density generator-matrix (LDGM) codes as syndrome measurement (SM) codes for quantum low-density parity check (QLDPC) codes. We use an efficient progressive-edge-growth-like algorithm to create LDGM SM…
Quantum error correction requires accurate and efficient decoding to optimally suppress errors in the encoded information. For concatenated codes, where one code is embedded within another, optimal decoding can be achieved using a…
In this work, we develop an efficient decoding method for graph codes, a class of stabilizer quantum error-correcting codes constructed from graph states. While optimal decoding is generally NP-hard, we propose a faster decoder exploiting…
In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted…
Protection of quantum information from noise is a massive challenge. One avenue people have begun to explore is reducing the number of particles needing to be protected from noise and instead use systems with more states, so called qudit…