Related papers: Simplified circuit-level decoding using Knill erro…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone…
Near term quantum computers suffer from the presence of different noise sources. In order to mitigate for this effect and acquire results with significantly better accuracy, there is the urge of designing efficient error correction or error…
Local decoders, also known as cellular-automaton decoders, offer a promising path toward real-time quantum error correction by replacing centralized classical decoding, with inherent hardware constraints, by a natively parallel and…
In this paper, we provise an implementation of five, seven and nine-qubits error correcting codes on a classical computer using the quantum simulator Feynman program. We also compare the three codes by computing the fidelity when double…
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…
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 becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
Recently a framework for assisted quantum error correction was proposed in which a specific type of error is allowed to occur on auxiliary qubits, which is in contrast to standard entanglement assistance that requires noiseless auxiliary…
Quantum error correction is essential for achieving fault-tolerant quantum computing. Gottesman-Kitaev-Preskill (GKP) codes are particularly effective at correcting continuous noise, such as Gaussian noise and loss, and can significantly…
Quantum error detection can produce unbiased expectation values that exponentially converge to noiseless results as the code distance is increased. Despite this, its performance as an error mitigation technique is relatively understudied on…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
Implementing algorithms on a fault-tolerant quantum computer will require fast decoding throughput and latency times to prevent an exponential increase in buffer times between the applications of gates. In this work we begin by quantifying…
Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome.…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
Lowering the resource overhead needed to achieve fault-tolerant quantum computation is crucial to building scalable quantum computers. We show that adapting conventional maximum likelihood (ML) decoders to a small subset of efficiently…