Related papers: Quantum error-correcting codes and their geometrie…
It is shown that the noise process in quantum computation can be described by spatially correlated decoherence and dissipation. We demonstrate that the conventional quantum error correcting codes correcting for single-qubit errors are…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
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…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error…
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…
The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
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…
The recently introduced detected-jump correcting quantum codes are capable of stabilizing qubit-systems against spontaneous decay processes arising from couplings to statistically independent reservoirs. These embedded quantum codes exploit…
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…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
It is important to protect quantum information against decoherence and operational errors, and quantum error-correcting (QEC) codes are the keys to solving this problem. Of course, just the existence of codes is not efficient. It is…
Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise…
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…
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…
This paper characterizes Goppa codes of certain maximal curves over finite fields defined by equations of the form $y^n = x^m + x$. We investigate Algebraic Geometric and quantum stabilizer codes associated with these maximal curves and…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…