Related papers: General tensor network decoding of 2D Pauli codes
We introduce an approach for estimating the expectation values of arbitrary $n$-qubit matrices $M \in \mathbb{C}^{2^n\times 2^n}$ on a quantum computer. In contrast to conventional methods like the Pauli decomposition that utilize $4^n$…
We consider the Additive White Gaussian Noise channel with Binary Phase Shift Keying modulation. Our aim is to enable an algebraic hard decision Bounded Minimum Distance decoder for a binary block code to exploit soft information obtained…
Neural-network decoders can achieve a lower logical error rate compared to conventional decoders, like minimum-weight perfect matching, when decoding the surface code. Furthermore, these decoders require no prior information about the…
Low density lattice codes (LDLC) are a family of lattice codes that can be decoded efficiently using a message-passing algorithm. In the original LDLC decoder, the message exchanged between variable nodes and check nodes are continuous…
Surface codes are the most promising candidates for fault-tolerant quantum computation. Single qudit errors are typically modelled as Pauli operators, to which general errors are converted via randomizing methods. In this Letter, we…
In this work, we propose a fully differentiable iterative decoder for quantum low-density parity-check (LDPC) codes. The proposed algorithm is composed of classical belief propagation (BP) decoding stages and intermediate graph neural…
Different choices of quantum error-correcting codes can reduce the demands on the physical hardware needed to build a quantum computer. To achieve the full potential of a code, we must develop practical decoding algorithms that can correct…
High-fidelity decoding of quantum error correction codes relies on an accurate experimental model of the physical errors occurring in the device. Because error probabilities can depend on the context of the applied operations, the error…
Future beyond-5G and 6G systems demand ultra-reliable, low-latency communication with short blocklengths, motivating the development of universal decoding algorithms. Guessing decoding, which infers the noise or codeword candidate in order…
The GKP encoding is a top contender among bosonic codes for fault-tolerant quantum computation. Analysis of the GKP code is complicated by the fact that finite-energy code states leak out of the ideal GKP code space and are not orthogonal.…
A rising problem in the compression of Deep Neural Networks is how to reduce the number of parameters in convolutional kernels and the complexity of these layers by low-rank tensor approximation. Canonical polyadic tensor decomposition…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less…
Quantum error correction (QEC) codes protect quantum information from errors due to decoherence. Many of them also serve as prototypical models for exotic topological quantum matters. Investigating the behavior of the QEC codes under…
Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with…
We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely…
We propose a general framework for decoding quantum error-correcting codes with generative modeling. The model utilizes autoregressive neural networks, specifically Transformers, to learn the joint probability of logical operators and…
Subspace codes were introduced by K\"otter and Kschischang for error control in random linear network coding. In this paper, a layered type of subspace codes is considered, which can be viewed as a superposition of multiple component…
In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further…
The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive. This in turn guarantees the existence of a quantum error correction code…