Related papers: Entanglement-Assisted Quantum Error Correction wit…
The increasing interest in using quantum error correcting codes in practical devices has heightened the need for designing quantum error correcting codes that can correct against specialized errors, such as that of amplitude damping errors…
An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to…
The entanglement-assisted (EA) formalism allows arbitrary classical linear codes to transform into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this…
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…
Long-distance optical quantum channels are necessarily lossy, leading to errors in transmitted quantum information, entanglement degradation and, ultimately, poor protocol performance. Quantum states carrying information in the channel can…
The main advantage of quantum metrology relies on the effective use of entanglement, which indeed allows us to achieve strictly better estimation performance over the standard quantum limit. In this paper, we propose an analogous method…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
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,…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…
We transfer the concept of linear feed-back shift registers to quantum circuits. It is shown how to use these quantum linear shift registers for encoding and decoding cyclic quantum error-correcting codes.
Recently, Lechner, Hauke and Zoller [Science Advances, 1(9)e1500838, (2015)] have proposed a quantum annealing architecture, in which a classical spin glass with all-to-all connectivity is simulated by a spin glass with geometrically local…
We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may…
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,…
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…
Traditional quantum error correction involves the redundant encoding of k quantum bits using n quantum bits to allow the detection and correction of any t bit error. The smallest general t=1 code requires n=5 for k=1. However, the dominant…
We present a general error-correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. Given any Ising model optimization problem, the encoding replaces each…
We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used…
We review some applications of entanglement to improve quantum measurements and communication, with the main focus on the optical implementation of quantum information processing. The evolution of continuos variable entangled states in…
It was shown by Ahn, Wiseman, and Milburn [PRA {\bf 67}, 052310 (2003)] that feedback control could be used as a quantum error correction process for errors induced by weak continuous measurement, given one perfectly measured error channel…
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a…