Related papers: Fast Decoders for Topological Quantum Codes
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…
The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by…
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…
Accurate decoding of quantum error-correcting codes is a crucial ingredient in protecting quantum information from decoherence. It requires characterizing the error channels corrupting the logical quantum state and providing this…
Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing…
The loss of qubits - the elementary carriers of quantum information - poses one of the fundamental obstacles towards large-scale and fault-tolerant quantum information processors. In this work, we experimentally demonstrate a complete…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
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…
We show that errors in data transmitted through linear codes can be thought of as codewords of minimum weight of new linear codes. To determine errors we can then use methods specific to finding such special codewords. One of these methods…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow…
We address the problem of performing message-passing-based decoding of quantum LDPC codes under hardware latency limitations. We propose a novel way to do layered decoding that suits quantum constraints and outperforms flooded scheduling,…
Real-time decoding of quantum error correction (QEC) is essential for enabling fault-tolerant quantum computation. A practical decoder must operate with high accuracy at low latency, while remaining robust to spatial and temporal variations…
Geometrically local quantum codes, which are error correction codes embedded in $\mathbb{R}^D$ with checks acting only on qubits within a fixed spatial distance, have garnered significant interest. Recently, it has been demonstrated how to…
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest…
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep…
In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications…
Post-selection strategies that discard low-confidence computational results can significantly improve the effective fidelity of quantum error correction at the cost of reduced acceptance rates, which can be particularly useful for offline…
Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC). This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes by…