Related papers: Optimal and Efficient Decoding of Concatenated Qua…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
Information obtained from noise characterization of a quantum device can be used in classical decoding algorithms to improve the performance of quantum error-correcting codes. Focusing on the surface code under local (i.e. single-qubit)…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
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 examine the performance of the single-mode GKP code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors. We show how one can optimize the tracking of errors in repeated noisy error…
We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes we analytically compute the effective logical channel that results when…
In this paper, we address the problem of designing a quantum encoder that maximizes the minimum output purity of a given decohering channel, where the minimum is taken over all possible pure inputs. This problem is cast as a max-min…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer.…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
Quantum error correction protocols have been developed to offset the high sensitivity to noise inherent in quantum systems. However, much is still unknown about the behaviour of a quantum error-correcting code under general noise, including…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
To well understand the behavior of quantum error correction codes (QECC) in noise processes, we need to obtain explicit coding maps for QECC. Due to extraordinary amount of computational labor that they entails, explicit coding maps are a…
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…
The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are…
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…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
In this paper, we propose a novel message-passing decoding approach that leverages the degeneracy of quantum low-density parity-check codes to enhance decoding performance, eliminating the need for serial scheduling or post-processing. Our…
The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…