Related papers: Fault Tolerant QR Factorization for General Matric…
Fault tolerance is essential for building reliable services; however, it comes at the price of redundancy, mainly the "replication factor" and "diversity". With the increasing reliance on Internet-based services, more machines (mainly…
In this paper, we address the challenge of learning with limited fault data for power transformers. Traditional operation and maintenance tools lack effective predictive capabilities for potential faults. The scarcity of extensive fault…
The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. In addition to preserving the data positivity property, it aims also to preserve…
In order to achieve fault-tolerant quantum computation, we need to repeat the following sequence of four steps: First, perform 1 or 2 qubit quantum gates (in parallel if possible). Second, do a syndrome measurement on a subset of the…
Instead of a quantum computer where the fundamental units are 2-dimensional qubits, we can consider a quantum computer made up of d-dimensional systems. There is a straightforward generalization of the class of stabilizer codes to…
I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011) for…
A scalable and programmable quantum computer holds the potential to solve computationally intensive tasks that classical computers cannot accomplish within a reasonable time frame, achieving quantum advantage. However, the vulnerability of…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
As Computed Tomography (CT) scans are an essential medical test, many techniques have been proposed to reconstruct high-quality images using a smaller amount of radiation. One approach is to employ algebraic factorization methods to…
The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…
Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new…
A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matrix multiplications, which greatly limits the benefits that…
A quantum computer -- i.e., a computer capable of manipulating data in quantum superposition -- would find applications including factoring, quantum simulation and tests of basic quantum theory. Since quantum superpositions are fragile, the…
The use of a few intermediate qutrits for efficient decomposition of 3-qubit unitary gates has been proposed, to obtain an exponential reduction in the depth of the decomposed circuit. An intermediate qutrit implies that a qubit is operated…
Achieving practical quantum advantage on fault-tolerant quantum computers (FTQC) is fundamentally constrained by the substantial spatial and temporal overheads required to map logical operations onto physical hardware. Existing compilation…
Shor's algorithm for integer factorization offers an exponential speedup over classical methods but remains impractical on Noisy Intermediate Scale Quantum (NISQ) hardware due to the need for many coherent qubits and very deep circuits.…
Proving threshold theorems for fault-tolerant quantum computation is a burdensome endeavor with many moving parts that come together in relatively formulaic but lengthy ways. It is difficult and rare to combine elements from multiple papers…
Continuous-Variable (CV) devices are a promising platform for demonstrating large-scale quantum information protocols. In this framework, we define a general quantum computational model based on a CV hardware. It consists of vacuum input…
An Adaptive Fault-tolerant Controller procedure for a class of the affine nonlinear system is developed in this paper. This methodology hides both the faults and external disturbances. Compare to the procedure that require separate fault…
Factorizing large matrices by QR with column pivoting (QRCP) is substantially more expensive than QR without pivoting, owing to communication costs required for pivoting decisions. In contrast, randomized QRCP (RQRCP) algorithms have proven…