相关论文: On Solving a Generalized Chinese Remainder Theorem…

In this paper, we derive new computational techniques for residue number systems (RNS) based Barrett algorithm (BA). The focus of the work is an algorithm that carries out the entire computation using only modular arithmetic without…

Using an adaptation of Qin Jiushao's method from the 13th century, it is possible to prove that a system of linear modular equations a(i,1) x(i) + ... + a(i,n) x(n) = b(i) mod m(i), i=1, ..., n has integer solutions if m(i)>1 are pairwise…

We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…

This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…

The emergence of ultra-wideband (UWB) and high-throughput signals has necessitated advancements in data sampling technologies1. Sub-Nyquist sampling methods, such as the modulated wideband converter (MWC) and compressed auto-correlation…

Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…

The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…

Quantum error mitigation schemes (QEM) have greatly enhanced the performance of quantum computers, mostly by reducing errors caused by interactions with the environment. Nevertheless, the presence of coherence errors, typically arising from…

In pulsed Doppler radars, the classic Chinese remainder theorem (CCRT) is a common method to resolve Doppler ambiguities caused by fast-moving targets. Another issue concerning high-velocity targets is related to the loss in the…

Quantum state tomography (QST), the process of reconstructing some unknown quantum state $\hat\rho$ from repeated measurements on copies of said state, is a foundationally important task in the context of quantum computation and simulation.…

Variations on a theorem of Cand\`es, Romberg and Tao The CRT theorem reconstructs a signal from a sparse set of frequencies, a paradigm of Compressed sensing. The signal is assumed to be carried by a small number of points, s, in a large…

Random linear network code has to sacrifice part of bandwidth to transfer the coding vectors, thus a head of size k log|T| is appended to each packet. We present a distributed random network coding approach based on the Chinese remainder…

We consider the problem of estimating the distance, or range, between two locations by measuring the phase of multiple sinusoidal signals transmitted between the locations. Traditional estimators developed for optical interferometry include…

The demands of accuracy in measurements and engineering models today, renders the condition number of problems larger. While a corresponding increase in the precision of floating point numbers ensured a stable computing, the uncertainty in…

It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum…

Quantum detector tomography (QDT) is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we utilize regularization to improve the QDT accuracy whenever the probe states are…

We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a…

We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a…

Amplitude estimation is a fundamental quantum algorithmic primitive that enables quantum computers to achieve quadratic speedups for a large class of statistical estimation problems, including Monte Carlo methods. The main drawback from the…

In this paper we present two efficient methods for reconstructing a rational number from several residue-modulus pairs, some of which may be incorrect. One method is a natural generalization of that presented by Wang, Guy and Davenport in…