Related papers: Quantum error correction in the presence of sponta…
Error correction, in the standard meaning of the term, implies the ability to correct all small analog errors and some large errors. Examining assumptions at the basis of the recently proposed quantum error-correcting codes, it is pointed…
We propose two quantum error correction schemes which increase the maximum storage time for qubits in a system of cold trapped ions, using a minimal number of ancillary qubits. Both schemes consider only the errors introduced by the…
A universal and fault tolerant scheme for quantum computation is proposed which utilizes a class of error correcting codes that is based on the detection of spontaneous emission (of, e.g., photons, phonons, and ripplons). The scheme is…
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…
A general theory of quantum error avoiding codes is established, and new light is shed on the relation between quantum error avoiding and correcting codes. Quantum error avoiding codes are found to be a special type of highly degenerate…
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 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 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…
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,…
A new method for quantum computation in the presence of detected spontaneous emission is proposed. The method combines strong and fast (dynamical decoupling) pulses and a quantum error correcting code that encodes $n$ logical qubits into…
A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…
We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…
We propose an error correction coding algorithm for continuous quantum variables. We use this algorithm to construct a highly efficient 5-wavepacket code which can correct arbitrary single wavepacket errors. We show that this class of…
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…
A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system.…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
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…
We propose a new approach to study the evolution of a quantum state that is encoded in a system which is continuously subject to the operations required to implement a quantum error correcting code. In the limit of continuous error…
We present for the first time a general theory of error correction for permutation invariant (PI) codes. Using representation theory of the symmetric group we construct efficient algorithms that can correct any correctible error on any PI…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…