Related papers: Quantum Block and Convolutional Codes from Self-or…
Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit…
Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
Given some group $G$ of logical gates, for instance the Clifford group, what are the quantum encodings for which these logical gates can be implemented by simple physical operations, described by some physical representation of $G$? We…
The hypergraph product (HGP) construction of quantum error-correcting codes (QECC) offers a general and explicit method for building a QECC from two classical codes, thereby paving the way for the discovery of good quantum low-density…
Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom…
We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by…
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…
We provide a construction for quantum codes (hermitian-self-orthogonal codes over GF(4)) starting from cyclic codes over GF(4^m). We also provide examples of these codes some of which meet the known bounds for quantum codes.
Quantum computing holds transformative potential for various fields, yet its practical application is hindered by the susceptibility to errors. This study makes a pioneering contribution by applying quantum error correction codes (QECCs)…
Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also…
In this paper, we present an error-trellis construction for tailbiting convolutional codes. A tailbiting error-trellis is characterized by the condition that the syndrome former starts and ends in the same state. We clarify the…
A self-correcting quantum memory is a type of quantum error correcting code that can correct errors passively through cooling. A major open question in the field is whether self-correcting quantum memories can exist in 3D. In this work, we…
The Hamiltonian model of quantum error correction code in the literature is often constructed with the help of its stabilizer formalism. But there have been many known examples of nonadditive codes which are beyond the standard quantum…
We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and…
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…
Quantum computers promise to solve certain problems exponentially faster than possible classically but are challenging to build because of their increased susceptibility to errors. Remarkably, however, it is possible to detect and correct…
We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite…
Kim et al. (2021) gave a method to embed a given binary $[n,k]$ code $\mathcal{C}$ $(k = 3, 4)$ into a self-orthogonal code of the shortest length which has the same dimension $k$ and minimum distance $d' \ge d(\mathcal{C})$. We extend this…
Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes $\mathcal{C}$, $\mathcal{D}$…