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Quantum degeneracy in error correction is a feature unique to quantum error correcting codes, unlike their classical counterpart. It allows a quantum error correcting code to correct errors even when they can not uniquely pinpoint the…
This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or…
Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. In NMR…
Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while…
From the set of operators for errors and its correction code, we introduce the so-called complete unitary transformation. It can be used for encoding while the inverse of it can be applied for correcting the errors of the encoded qubit. We…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4…
This paper addresses and expands on the contents of the recent Letter [Phys. Rev. Lett. 111, 030502 (2013)] discussing private quantum subsystems. Here we prove several previously presented results, including a condition for a given random…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
In this paper, we assume an error such that a single insertion occurs and then a single deletion occurs. Under such an error model, this paper provides a decoding algorithm for non-binary quantum codes constructed by Matsumoto and Hagiwara.
Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
The development of high-resolution, large-baseline optical interferometers would revolutionize astronomical imaging. However, classical techniques are hindered by physical limitations including loss, noise, and the fact that the received…
Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric $n$-vertices colourable graph and a group of operations (colouring rules) on the graph: find the minimum sequence…
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by…
Graph states have been used for quantum error correction by Schlingemann et al. [Physical Review A 65.1 (2001): 012308]. Hypergraph states [Physical Review A 87.2 (2013): 022311] are generalizations of graph states and they have been used…
The entanglement of formation gives a necessary and sufficient condition for the existence of a perfect quantum error correction procedure.
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we give a detailed account of recent results in which we showed that topological quantum memories can simultaneously tolerate both loss…