Related papers: Generalized Short Path Algorithms: Towards Super-Q…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
Quantum state tomography (QST) allows for the reconstruction of quantum states through measurements and some inference technique under the assumption of repeated state preparations. Bayesian inference provides a promising platform to…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…
In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…
Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…
Linear regression is one of the most fundamental linear algebra problems. Given a dense matrix $A \in \mathbb{R}^{n \times d}$ and a vector $b$, the goal is to find $x'$ such that $ \| Ax' - b \|_2^2 \leq (1+\epsilon) \min_{x} \| A x - b…
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…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
We develop a quantum-classical hybrid algorithm for function optimization that is particularly useful in the training of neural networks since it makes use of particular aspects of high-dimensional energy landscapes. Due to a recent…
We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection…
We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine…
We assess the prospects for algorithms within the general framework of quantum annealing (QA) to achieve a quantum speedup relative to classical state of the art methods in combinatorial optimization and related sampling tasks. We argue for…
Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by…
We present a centralized algorithmic framework for solving multi-robot path planning problems in general, two-dimensional, continuous environments while minimizing globally the task completion time. The framework obtains high levels of…
In this study, we present a simple and intuitive method for accelerating optimal Reeds-Shepp path computation. Our approach uses geometrical reasoning to analyze the behavior of optimal paths, resulting in a new partitioning of the state…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
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 complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…