Related papers: Diagnosis of weaknesses in modern error correction…
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.…
Here we develop an approach to predict power grid weak points, and specifically to efficiently identify the most probable failure modes in static load distribution for a given power network. This approach is applied to two examples: Guam's…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
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…
To address the issue of increased bit error rates during the later stages of linear search in denoising diffusion error correction codes, we propose a novel method that optimizes denoising diffusion error correction codes (ECC) using cosine…
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg…
Storage systems have a strong need for substantially improving their error correction capabilities, especially for long-term storage where the accumulating errors can exceed the decoding threshold of error-correcting codes (ECCs). In this…
Quantum computing, which has the power to accelerate many computing applications, is currently a technology under development. As a result, the existing noisy intermediate-scale quantum (NISQ) computers suffer from different hardware noise…
Data assimilation performance can be significantly impacted by biased noise in observations, altering the signal magnitude and introducing fast oscillations or discontinuities when the system lacks smoothness. To mitigate these issues, this…
Fault Trees represent an essential tool in the reliability and risk assessment of engineering systems. By decomposing the structure of the system into Boolean function, Fault Trees allow the quantitative and qualitative analysis of the…
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…
In this article, we introduce a new technique for precision tuning. This problem consists of finding the least data types for numerical values such that the result of the computation satisfies some accuracy requirement. State of the art…
The behavior of real quantum hardware differs strongly from the simple error models typically used when simulating quantum error correction. Error processes are far more complex than simple depolarizing noise applied to single gates, and…
We discretize the stochastic Allen-Cahn equation with additive noise by means of a spectral Galerkin method in space and a tamed version of the exponential Euler method in time. The resulting error bounds are analyzed for the…
In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
The persistent storage of big data requires advanced error correction schemes. The classical approach is to use error correcting codes (ECCs). This work studies an alternative approach, which uses the redundancy inherent in data itself for…
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,…
We develop a classical bit-flip correction method to mitigate measurement errors on quantum computers. This method can be applied to any operator, any number of qubits, and any realistic bit-flip probability. We first demonstrate the…