Related papers: A streamlined quantum algorithm for topological da…

Despite significant effort, the quantum machine learning community has only demonstrated quantum learning advantages for artificial cryptography-inspired datasets when dealing with classical data. In this paper we address the challenge of…

Though there has been substantial progress in developing quantum algorithms to study classical datasets, the cost of simply \textit{loading} classical data is an obstacle to quantum advantage. When the amplitude encoding is used, loading an…

Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…

Dynamical systems appear in nearly every aspect of the physical world. As such, understanding the properties of dynamical systems is of great importance. Typically, a dynamical system is described by a system of ordinary differential…

Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…

Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…

We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of basic semialgebraic sets which works in weak exponential time. That is, out of a set of exponentially small measure in the space of…

The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…

Convolutional neural network is a crucial tool for machine learning, especially in the field of computer vision. Its unique structure and characteristics provide significant advantages in feature extraction. However, with the exponential…

This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are…

We contrast a minimalistic implementation of quantum k-means algorithm to classical k-means algorithm. With classical simulation results, we demonstrate a quantum performance, on and above par, with the classical k-means algorithm. We…

We consider quantum-classical hybrid machine learning in which large-scale input channels remain classical and small-scale working channels process quantum operations conditioned on classical input data. This does not require the conversion…

We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…

We present a quantum algorithm for computing the Ramsey numbers whose computational complexity grows super-exponentially with the number of vertices of a graph on a classical computer. The problem is mapped to a decision problem on a…

We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…

Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale…

Building on the quantum ensemble based classifier algorithm of Schuld and Petruccione [arXiv:1704.02146v1], we devise equivalent classical algorithms which show that this quantum ensemble method does not have advantage over classical…

In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…

Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…

Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…