Related papers: Neural Decoder for Topological Codes using Pseudo-…

There has been a rise in decoding quantum error correction codes with neural network based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger…

We consider near maximum-likelihood (ML) decoding of short linear block codes based on neural belief propagation (BP) decoding recently introduced by Nachmani et al.. While this method significantly outperforms conventional BP decoding, the…

The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…

In this paper, we propose a new coded computing technique called "substitute decoding" for general iterative distributed computation tasks. In the first part of the paper, we use PageRank as a simple example to show that substitute decoding…

In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated…

We introduce a family of 2D topological subsystem quantum error-correcting codes. The gauge group is generated by 2-local Pauli operators, so that 2-local measurements are enough to recover the error syndrome. We study the computational…

Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…

We present a nonintrusive method for reliably estimating the noise level during quantum computation and quantum communication protected by quantum error-correcting codes. As preprocessing of quantum error correction, our scheme estimates…

In a recent work, Bombin, Duclos-Cianci, and Poulin showed that every local translationally invariant 2D topological stabilizer code is locally equivalent to a finite number of copies of Kitaev's toric code. For 2D color codes, Delfosse…

We propose a novel decoding approach for neural machine translation (NMT) based on continuous optimisation. We convert decoding - basically a discrete optimization problem - into a continuous optimization problem. The resulting constrained…

An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS…

Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching (MWPM) based methods. Recent advances have shown that topological codes can be…

Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…

In this work, we investigate the problem of neural-based error correction decoding, and more specifically, the new so-called syndrome-based decoding technique introduced to tackle scalability in the training phase for larger code sizes. We…

Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this…

Fast, reliable decoders are pivotal components for enabling fault-tolerant quantum computation. Neural network decoders like AlphaQubit have demonstrated significant potential, achieving higher accuracy than traditional human-designed…

Image denoising methods must effectively model, implicitly or explicitly, the vast diversity of patterns and textures that occur in natural images. This is challenging, even for modern methods that leverage deep neural networks trained to…

We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…

Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity. Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where…

A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…