相关论文: Good Quantum Convolutional Error Correction Codes …
Quantum Error Correction (QEC) is essential for fault-tolerant quantum copmutation, and its implementation is a very sophisticated process involving both quantum and classical hardware. Formulating and verifying the decomposition of logical…
The article surveys quantum error control, focusing on quantum stabilizer codes, stressing on the how to use classical codes to design good quantum codes. It is to appear as a book chapter in "A Concise Encyclopedia of Coding Theory,"…
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral…
We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding…
Quantum error correction is essential for realizing scalable quantum computation. Among various approaches, low-density parity-check codes over higher-order Galois fields have shown promising performance due to their structured sparsity and…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…
The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure,…
Quantum computers have the possibility of a much reduced calculation load compared with classical computers in specific problems. Quantum error correction (QEC) is vital for handling qubits, which are vulnerable to external noise. In QEC,…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
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…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…
We identify gauge freedoms in quantum error correction (QEC) codes and introduce strategies for optimal control algorithms to find the gauges which allow the easiest experimental realization. Hereby, the optimal gauge depends on the…
Current approaches to fault-tolerant quantum computation will not enable useful quantum computation on near-term devices of 50 to 100 qubits. Leading proposals, such as the color code and surface code schemes, must devote a large fraction…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes.…
We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…