Related papers: Entanglement-assisted codeword stabilized quantum …
Quantum error-correction codes would protect an arbitrary state of a multi-qubit register against decoherence-induced errors, but their implementation is an outstanding challenge for the development of large-scale quantum computers. A first…
Superdense Coding is a cornerstone in secure quantum communication, exploiting pre-shared entanglement to encode two classical bits within a single qubit. However, noise and decoherence deteriorate entanglement quality, restricting both…
We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code.…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable…
Quantum error correction protects logical quantum information against environmental decoherence by encoding logical qubits into entangled states of physical qubits. One of the most important near-term challenges in building a scalable…
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…
We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit,…
For every stabiliser $N$-qudit absolutely maximally entangled state, we present a method for determining the stabiliser generators and logical operators of a corresponding quantum error correction code. These codes encode $k$ qudits into…
This paper develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum…
Codeword stabilized (CWS) codes are, in general, non-additive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical non-linear codes. For an n-qubit quantum…
We consider classical message transmission under entanglement assistance for compound memoryless and arbitrarily varying quantum channels. In both cases, we prove general coding theorems together with corresponding weak converse bounds. In…
Entanglement represents one of the most important conceptual advances in physics during the last century and is also one of the most essential resources in quantum information science. However, entanglement is fragile and its potential…
We provide a self-contained introduction for entanglement-assisted quantum error-correcting codes in this book chapter.
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by analyzing the cyclotomic cosets in the defining set of constacyclic codes, we constructed…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…
The five-qubit quantum error correcting code encodes one logical qubit to five physical qubits, and protects the code from a single error. It was one of the first quantum codes to be invented, and various encoding circuits have been…