Related papers: Continuous Error Correction
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it…
I give an overview of the basic concepts behind quantum error correction and quantum fault tolerance. This includes the quantum error correction conditions, stabilizer codes, CSS codes, transversal gates, fault-tolerant error correction,…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Operator quantum error correction is a recently developed theory that provides a generalized framework for active error correction and passive error avoiding schemes. In this paper, we describe these codes in the stabilizer formalism of…
We consider the evolution of open quantum systems coupled to one or more Gaussian environments. We demonstrate that such systems can be described by a Markovian quantum master equation (MQME) up to a correction that decreases exponentially…
The storage and processing of quantum information are susceptible to external noise, resulting in computational errors that are inherently continuous A powerful method to suppress these effects is to use quantum error correction. Typically,…
In this paper an extended scalability condition is proposed to achieve the ground-state stability for a class of multipartite quantum systems which may involve two-body interactions, and an explicit procedure to construct the dissipation…
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
Quantum error-correction routines are developed for continuous quantum variables such as position and momentum. The result of such analog quantum error correction is the construction of composite continuous quantum variables that are…
Open quantum systems are a topic of intense theoretical research. The use of master equations to model a system's evolution subject to an interaction with an external environment is one of the most successful theoretical paradigms. General…
Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. In NMR…
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…
Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of…
A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…