Related papers: Quantum Speedups for Exponential-Time Dynamic Prog…

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…

We study the traveling salesman problem in the hyperbolic plane of Gaussian curvature $-1$. Let $\alpha$ denote the minimum distance between any two input points. Using a new separator theorem and a new rerouting argument, we give an…

We first show that the Traveling Salesman Problem in an n-vertex graph with average degree bounded by d can be solved in O*(2^{(1-\eps_d)n}) time and exponential space for a constant \eps_d depending only on d, where the O*-notation…

The main approach to hybrid quantum-classical neural networks (QNN) is employing quantum computing to build a neural network (NN) that has quantum features, which is then optimized classically. Here, we propose a different strategy: to use…

Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ to minimize the radius of the resulting graph. Previously, a similar problem for minimizing the diameter of the graph…

Quantum search algorithms, such as Grover's algorithm, are anticipated to efficiently solve constrained combinatorial optimization problems. However, applying these algorithms to the traveling salesman problem (TSP) on a quantum circuit…

We present a quantum algorithm for simulating the classical dynamics of $2^n$ coupled oscillators (e.g., $2^n$ masses coupled by springs). Our approach leverages a mapping between the Schr\"odinger equation and Newton's equation for…

Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…

In this paper, it is demonstrated that the DNA-based algorithm [Ho et al. 2005] for solving an instance of the clique problem to any a graph G = (V, E) with n vertices and p edges and its complementary graph G1 = (V, E1) with n vertices and…

Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…

We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…

A new characterization of Hamiltonian graphs using f-cutset matrix is proposed. Based on this new characterization, a new exact polynomial time algorithm for the traveling salesman problem (TSP) is developed. We then define the so-called…

We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley. We show that there exists a whole class of quantum search algorithms in the symmetry reduced…

Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…

Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…

One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…

Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand…

In previous research, quantum resources were concretely estimated for solving Elliptic Curve Discrete Logarithm Problem(ECDLP). In [1], the quantum algorithm was optimized for the binary elliptic curves and the main optimization target was…

One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)], finds a marked…

The famous Travelling Salesman Problem (TSP) is an important category of optimization problems that is mostly encountered in various areas of science and engineering. Studying optimization problems motivates to develop advanced techniques…