Related papers: Quantum speedups for linear programming via interi…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine…
Solving linear systems of equations is a frequently encountered problem in machine learning and optimisation. Given a matrix $A$ and a vector $\mathbf b$ the task is to find the vector $\mathbf x$ such that $A \mathbf x = \mathbf b$. We…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…
We investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive…
In this paper we provide an $\tilde{O}(nd+d^{3})$ time randomized algorithm for solving linear programs with $d$ variables and $n$ constraints with high probability. To obtain this result we provide a robust, primal-dual…
We propose an adaptive random quantum algorithm to obtain an optimized eigensolver. Specifically, we introduce a general method to parametrize and optimize the probability density function of a random number generator, which is the core of…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
We describe a general method to obtain quantum speedups of classical algorithms which are based on the technique of backtracking, a standard approach for solving constraint satisfaction problems (CSPs). Backtracking algorithms explore a…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
We give two quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with $m$ constraint matrices, each of dimension $n$, rank at most $r$, and sparsity $s$. The first algorithm…
In this paper we provide faster algorithms for solving the geometric median problem: given $n$ points in $\mathbb{R}^{d}$ compute a point that minimizes the sum of Euclidean distances to the points. This is one of the oldest non-trivial…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Gradient-based algorithms are one of the methods of choice for the optimisation of Markov Decision Processes. In this article we will present a novel approximate Newton algorithm for the optimisation of such models. The algorithm has…