Related papers: Quantum Error Correction and Fault-Tolerance
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the…
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…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
We describe a method to execute globally controlled quantum information processing which admits a fault tolerant quantum error correction scheme. Our scheme nominally uses three species of addressable two-level systems which are arranged in…
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 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…
We describe a fault-tolerant one-way quantum computer on cluster states in three dimensions. The presented scheme uses methods of topological error correction resulting from a link between cluster states and surface codes. The error…
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph…
Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…
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.…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are…
This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or…
Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple…