Related papers: Approximate quantum error correction
Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical…
Numerous quantum many-body systems are characterized by either fundamental or emergent constraints---such as gauge symmetries or parity superselection for fermions---which effectively limit the accessible observables and realizable…
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 consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian…
Certain physical aspects of quantum error correction are discussed for a quantum computer (n-qubit register) in contact with a decohering environment. Under rather plausible assumptions upon the form of the computer-environment interaction,…
The essence of quantum error-correction is to use redundant Hilbert space to identify and correct errors, and the channel fidelity of the quantum channel does not affect which errors can be identified and corrected. Based on this, it is…
We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate…
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…
Quantum error correction assisted by entanglement helps to transmit the encoded qudits through quantum channels with some of them being noiseless. Here we consider a more realistic scheme for experiments what we called as partial-noisy…
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…
It is shown that quantum tomography can detect and correct unlimited number of errors during the evaluation of quantum algorithms on quantum computer.
In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the…
A family of high rate quantum error correcting codes adapted to the amplitude damping channel is presented. These codes are nonadditive and exploit self-complementarity structure to correct all first-order errors. Their rates can be higher…
The task of determining whether a given quantum channel has positive capacity to transmit quantum information is a fundamental open problem in quantum information theory. In general, the coherent information needs to be computed for an…
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…
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…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
It is important to study the behavior of a t-error correcting quantum code when the number of errors is greater than t, because it is likely that there are also small errors besides t large correctable errors. We give a lower bound for the…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case…