Related papers: A Modified MWPM Decoding Algorithm for Quantum Sur…
Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code. Using such circuits for the surface code requires decoding…
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…
We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or…
Recently, quantum error-correcting codes were proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit flip and phase flip errors. An example for a channel which…
Fast classical processing is essential for most quantum fault-tolerance architectures. We introduce a sliding-window decoding scheme that provides fast classical processing for the surface code through parallelism. Our scheme divides the…
The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that…
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…
With the advent of noisy intermediate-scale quantum (NISQ) devices, practical quantum computing has seemingly come into reach. However, to go beyond proof-of-principle calculations, the current processing architectures will need to scale up…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
We present techniques that improve the performance of asymmetric stabilizer codes in the presence of unital channels with unknown parameters. Our method estimates the channel parameters using information recovered from syndrome measurements…
In this work, we introduce a fast implementation of the minimum-weight perfect matching (MWPM) decoder, the most widely used decoder for several important families of quantum error correcting codes, including surface codes. Our algorithm,…
Practical applications of quantum computing depend on fault-tolerant devices with error correction. Today, the most promising approach is a class of error-correcting codes called surface codes. We study the problem of compiling quantum…
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…
In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary…
In the implementation of quantum information systems, one type of Pauli error, such as phase-flip errors, may occur more frequently than others, like bit-flip errors. For this reason, quantum error-correcting codes that handle asymmetric…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
The surface code is one of the leading quantum error correction codes for realizing large-scale fault-tolerant quantum computing (FTQC). One major challenge in realizing surface-code-based FTQC is the extremely large number of qubits…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…