Related papers: Nonadditive quantum error correcting codes adapted…
In quantum error correction, it is an important assumption that errors on different qubits are independent. In our previous work [Phys. Rev. A {\bf 92}, 052320 (2015)], the generality of the concatenated five-qubit code has been investgated…
We introduce and initiate the study of a family of higher rank matricial ranges, taking motivation from hybrid classical and quantum error correction coding theory and its operator algebra framework. In particular, for a noisy quantum…
We develop a new approach for asymmetric LDPC-based information reconciliation in order to adapt to the current channel state and achieve better performance and scalability in practical resource-constrained QKD systems. The new scheme…
Up to now every good quantum error-correcting code discovered has had the structure of an eigenspace of an Abelian group generated by tensor products of Pauli matrices; such codes are known as stabilizer or additive codes. In this letter we…
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,…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
We show how procedures which can correct phase and amplitude errors can be directly applied to correct errors due to quantum entanglement. We specify general criteria for quantum error correction, introduce quantum versions of the Hamming…
Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is…
When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very…
Quantum error correction of a surface code or repetition code requires the pairwise matching of error events in a space-time graph of qubit measurements, such that the total weight of the matching is minimized. The input weights follow from…
The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive. This in turn guarantees the existence of a quantum error correction code…
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a…
In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of…
Error correcting codes protect quantum information and form the basis of fault tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transverse non-Clifford…
This paper explores the possibilities and limitations of error correction by the structural simplicity of error mechanisms. Specifically, we consider channel models, called \emph{samplable additive channels}, in which (a) errors are…
We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…
Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such…
In this work we prove that the 5-qubit quantum error correcting code does not fix qubit independent errors, even assuming that the correction circuit does not introduce new errors. We say that a quantum code does not fix a quantum computing…
Designing efficient fault tolerance schemes is crucial for building useful quantum computers. Most standard schemes assume no knowledge of the underlying device noise and rely on general-purpose quantum error-correcting (QEC) codes capable…
In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…