Related papers: General tensor network decoding of 2D Pauli codes
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…
Quantum error correction (QEC) is essential for fault-tolerant quantum computation. Often in QEC errors are assumed to be independent and identically distributed and can be discretised to a random Pauli error during the execution of a…
The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome…
Stabilizer-based simulation of quantum error-correcting codes typically relies on the Pauli-twirling approximation (PTA) to render non-Clifford noise classically tractable, but PTA can distort the behavior of physically relevant channels…
Polar codes have been adopted as the control channel coding scheme in the fifth generation new radio (5G NR) standard due to its capacity-achievable property. Traditional polar decoding algorithms such as successive cancellation (SC) suffer…
We introduce an efficient decoder of the color code in $d\geq 2$ dimensions, the Restriction Decoder, which uses any $d$-dimensional toric code decoder combined with a local lifting procedure to find a recovery operation. We prove that the…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
The use of quantum computation for wireless network applications is emerging as a promising paradigm to bridge the performance gap between in-practice and optimal wireless algorithms. While today's quantum technology offers limited number…
In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based…
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…
Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit,…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
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 consider binary systematic network codes and investigate their capability of decoding a source message either in full or in part. We carry out a probability analysis, derive closed-form expressions for the decoding probability and show…
We introduce a decoder for the 3D color code with boundaries, which is a variation of the restriction decoder introduced by Kubicka and Delfosse. Specifically, we adapt the lift procedure to efficiently find a correction on qubits adjacent…
Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes,…
We consider tensor-network stabilizer codes and show that their tensor-network decoder has the property that independent logical qubits can be decoded in parallel. As long as the error rate is below threshold, we show that this parallel…
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be…
Recently, a parallel decoding framework of $G_N$-coset codes was proposed. High throughput is achieved by decoding the independent component polar codes in parallel. Various algorithms can be employed to decode these component codes,…
It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum…