相关论文: Concatenated Quantum Codes Constructible in Polyno…
We introduce a novel framework for implementing error-correction in constrained systems. The main idea of our scheme, called Quantized-Constraint Concatenation (QCC), is to employ a process of embedding the codewords of an error-correcting…
We discuss single-shot decoding of quantum Calderbank-Shor-Steane codes with faulty syndrome measurements. We state the problem as a joint source-channel coding problem. By adding redundant rows to the code's parity-check matrix we obtain…
In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings.…
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
We show how to construct a large class of quantum error correcting codes, known as CSS codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger…
In this paper, we propose a novel message-passing decoding approach that leverages the degeneracy of quantum low-density parity-check codes to enhance decoding performance, eliminating the need for serial scheduling or post-processing. Our…
One of the main problems for the future of practical quantum computing is to stabilize the computation against unwanted interactions with the environment and imperfections in the applied operations. Existing proposals for quantum memories…
We examine the transformation of noise under a quantum error correcting code (QECC) concatenated repeatedly with itself, by analyzing the effects of a quantum channel after each level of concatenation using recovery operators that are…
We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted…
Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance. A natural question concerns the efficient decodability of these codes. In this paper, we present a linear…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
We define code maps between Calderbank-Shor-Steane (CSS) codes using maps between chain complexes, and describe code surgery between such codes using a specific colimit in the category of chain complexes. As well as describing a surgery…
Different quantum error correction schemes trade off overhead, error suppression, and hardware connectivity. Code concatenation can relax these tradeoffs by using an outer code whose non-local connectivity is supplied by logical operations…
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…
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…
Quantum low-density parity-check (QLDPC) codes provide a practical balance between error-correction capability and implementation complexity in quantum error correction (QEC). In this paper, we propose an algebraic construction based on…
The quantum paradigm presents a phenomenon known as degeneracy that should improve the performance of quantum error correcting codes. However, the effects of this mechanism are sometimes ignored when evaluating the performance of sparse…
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…
Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum…