Related papers: Theory of Quantum Error Correction for General Noi…
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…
Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such…
In this introduction we motivate and explain the ``decoding'' and ``subsystems'' view of quantum error correction. We explain how quantum noise in QIP can be described and classified, and summarize the requirements that need to be satisfied…
The concept of multiple particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer.…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
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…
There are two complementary approaches to realizing quantum information so that it is protected from a given set of error operators. Both involve encoding information by means of subsystems. One is initialization-based error protection,…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
A major obstacle towards realizing a practical quantum computer is the noise that arises due to system-environment interactions. While it is very well known that quantum error correction (QEC) provides a way to protect against errors that…
Quantum error correction is essential for robust quantum information processing with noisy devices. As bosonic quantum systems play a crucial role in quantum sensing, communication, and computation, it is important to design error…
Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can…
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…
The theory of quantum error correction is a cornerstone of quantum information processing. It shows that quantum data can be protected against decoherence effects, which otherwise would render many of the new quantum applications…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for…
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg…
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by…