相关论文: Solving Shift Problems and Hidden Coset Problem Us…
We consider a version of Shor's quantum factoring algorithm such that the quantum Fourier transform is replaced by an extremely simple one where decomposition coefficients take only the values of $1,i,-1,-i$. In numerous calculations which…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
How can we take inspiration from a typical quantum algorithm to design heuristics for machine learning? A common blueprint, used from Deutsch-Josza to Shor's algorithm, is to place labeled information in superposition via an oracle,…
It is pointed out that an exactly solvable permutation operator, viewed as the quantization of cyclic shifts, is useful in constructing a basis in which to study the quantum baker's map, a paradigm system of quantum chaos. In the basis of…
This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer…
The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
In this paper an extension of the sparse decomposition problem is considered and an algorithm for solving it is presented. In this extension, it is known that one of the shifted versions of a signal s (not necessarily the original signal…
Recently, a new polynomial basis over binary extension fields was proposed such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order $\mathcal{O}(n\lg(n))$, where $n$ is the number of points…
A new quantum algorithm is proposed to solve Satisfiability(SAT) problems by taking advantage of non-unitary transformation in ground state quantum computer. The energy gap scale of the ground state quantum computer is analyzed for 3-bit…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
This work is a follow up on the newly proposed clustering algorithm called The Inverse Square Mean Shift Algorithm. In this paper a special case of algorithm for dealing with non-homogenous data is formulated and the three dimensional Fast…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
We propose a novel decoding approach for neural machine translation (NMT) based on continuous optimisation. We convert decoding - basically a discrete optimization problem - into a continuous optimization problem. The resulting constrained…
The JPEG algorithm compresses a digital image by filtering its high spatial-frequency components. Similarly, we introduce a quantum algorithm that uses the quantum Fourier transform to discard the high spatial-frequency qubits of an image,…
We propose a method for solving the hidden subgroup problem in nilpotent groups. The main idea is iteratively transforming the hidden subgroup to its images in the quotient groups by the members of a central series, eventually to its image…
Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
The problem of inhomogeneous cluster densities has been a long-standing issue for distance-based and density-based algorithms in clustering and anomaly detection. These algorithms implicitly assume that all clusters have approximately the…