Related papers: An efficient quantum algorithm for spectral estima…

Random quantum circuit sampling serves as a benchmark to demonstrate quantum computational advantage. Recent progress in classical algorithms, especially those based on tensor network methods, has significantly reduced the classical…

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…

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based…

What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…

High-dimensional datasets typically cluster around lower-dimensional manifolds but are also often marred by severe noise, obscuring the intrinsic geometry essential for downstream learning tasks. We present a quantum algorithm for…

Methods of processing quantum data become more important as quantum computing devices improve their quality towards fault tolerant universal quantum computers. These methods include discrimination and filtering of quantum states given as an…

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.…

Quantum reservoir computing has emerged as a promising machine learning paradigm for processing temporal data on near-term quantum devices, as it allows for exploiting the large computational capacity of the qubits without suffering from…

In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…

Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of…

By means of a simple example it is demonstrated that the task of finding and identifying certain patterns in an otherwise (macroscopically) unstructured picture (data set) can be accomplished efficiently by a quantum computer. Employing the…

Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…

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 propose quantum subroutines for the simplex method that avoid classical computation of the basis inverse. We show how to quantize all steps of the simplex algorithm, including checking optimality, unboundedness, and identifying a pivot…

We present a novel approach for the problem of frequency estimation in data streams that is based on optimization and machine learning. Contrary to state-of-the-art streaming frequency estimation algorithms, which heavily rely on random…

The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…

In quantum kernel learning, the primary method involves using a quantum computer to calculate the inner product between feature vectors, thereby obtaining a Gram matrix used as a kernel in machine learning models such as support vector…

The application of quantum computing to the field of image processing has produced several promising applications: quantum image representation techniques have been developed showing how, by taking advantage of quantum properties like…

Gibbs sampling from continuous real-valued functions is a challenging problem of interest in machine learning. Here we leverage quantum Fourier transforms to build a quantum algorithm for this task when the function is periodic. We use the…

We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues…