Related papers: A quantum algorithm for greatest common divisor pr…
Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…
Shor's algorithm efficiently solves factoring and discrete logarithm problems using quantum computers, compromising all public key schemes used today. These schemes rely on assumptions on their computational complexity, which quantum…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
In this work, we present a multi-layer quantum search method that generates an exponential speedup of the standard Grover's algorithm. As direct applications, any NP problems can be solved efficiently on a quantum circuit with only…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size…
Finding the optimal solution to a complex optimization problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
Simulating quantum computation on a classical computer is a difficult problem. The matrices representing quantum gates, and the vectors modeling qubit states grow exponentially with an increase in the number of qubits. However, by using a…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
Considering the difficult problem under classical computing model can be solved by the quantum algorithm in polynomial time, t-multiple discrete logarithm problems presented. The problem is non-degeneracy and unique solution. We talk about…
The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry,…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is…
Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…
Shor's quantum algorithm for discrete logarithms applied to elliptic curve groups forms the basis of a "quantum attack" of elliptic curve cryptosystems. To implement this algorithm on a quantum computer requires the efficient implementation…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…