International Business Machines Corporation

Lucent Technologies Inc.

Alcatel-lucent USA Inc.

Kenneth Lee Clarkson

Lior Horesh

Mark Steven Squillante

David Paul Woodruff

Vasileios Kalantzis

Ismail Yunus Akhalwaya

Shashanka Ubaru

Tal Kachman

John D Hobby

Karl Georg Hampel

Paul Anthony Polakos

Daniel Gruhl

John A Gunnels

Neal Ryan Lewis

Nimrod Megiddo

Alfredo Alba

James Harvey Kaufman

Wim Sweldens

Clemens Drews

Cartic Ramakrishnan

Meenakshi Nagarajan

Giacomo Nannicini

Haim Avron

Ronald Fagin

Jayram S Thathachar

Pablo N Mendes

Alice Zheng

Mark Kunitomi

Srinivasan Keshav

Matthew Aaron Davis

Georgios Kollias

Cristina Cornelio

Paul Matthew Mankiewich

David Tse

Matthias Grossglauser

Huy Le Nguyen

Sara Magliacane

A quantum computer-implemented system, method, and computer program product for quantum topological domain analysis (QTDA). The QTDA method achieves an improved exponential speedup and depth complexity of O(n log(1/(δ∈))) where n is the number of data points, ∈ is the error tolerance, δ is the smallest nonzero eigenvalue of the restricted Laplacian, and achieves quantum advantage on general classical data. The QTDA system and method efficiently realizes a combinatorial Laplacian as a sum of Pauli operators; performs a quantum rejection sampling and projection approach to build the relevant simplicial complex repeatedly and restrict the superposition to the simplices of a desired order in the complex; and estimates Betti numbers using a stochastic trace/rank estimation method that does not require Quantum Phase Estimation. The quantum circuit and QTDA method exhibits computational time and depth complexities for Betti number estimation up to an error tolerance ∈.

Linear-depth quantum system for topological data analysis

Techniques and a system to facilitate estimation of a quantum phase, and more specifically, to facilitate estimation of an expectation value of a quantum state, by utilizing a hybrid of quantum and classical methods are provided. In one example, a system is provided. The system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can include an encoding component and a learning component. The encoding component can encode an expectation value associated with a quantum state. The learning component can utilize stochastic inference to determine the expectation value based on an uncollapsed eigenvalue pair.

Short-depth active learning quantum amplitude estimation without eigenstate collapse

A system, method, and computer program product are disclosed. The method includes loading a first set of data as an initial matrix and determining a truncated singular value decomposition (SVD) of the initial matrix. The method also includes loading a second set of data as a new matrix, generating a first projection matrix, which approximates k leading left singular vectors of the updated matrix, and generating a second projection matrix, which approximates k leading right singular vectors of the updated matrix. Further, the method includes determining based on the initial matrix, the new matrix, the SVD of the existing matrix, and the first or second projection matrix, an approximate truncated SVD of the updated matrix.

Projection-based techniques for updating singular value decomposition in evolving data sets

A method for performing sparse quantum Fourier transform computation includes defining a set of quantum circuits, each quantum circuit comprising a Hadamard gate and a single frequency rotation operator, said set of quantum circuits being equivalent to a quantum Fourier transform circuit. The method includes constructing a subset of said quantum circuits in a quantum processor, said quantum processor having a quantum representation of a classical distribution loaded into a quantum state of said quantum processor. The method includes executing said subset of said quantum circuits on said quantum state, and performing a measurement in a frequency basis to obtain a frequency distribution corresponding to said quantum state.

Quantum sparse Fourier transform

Systems, computer-implemented methods, and computer program products that can facilitate quantum topological classification are described. According to an embodiment, a system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise a topological component that employs one or more quantum computing operations to identify one or more persistent homology features of a topological simplicial structure. The computer executable components can further comprise a topological classifier component that employs one or more machine learning models to classify the topological simplicial structure based on the one or more persistent homology features.

Quantum topological classification

A method for optimal design of experiments for joint model selection and parametrization determination of a symbolic mathematical model includes: determining a prediction value for a given inquiry data point, functional form and parameterization for conducting an experiment relating to a system under investigation; assuming a set of input-output data pairs as a starting point in a model discovery process relating to the system under investigation; performing discovery of symbolic models minimizing complexity for a bounded misfit, or minimizing a misfit measure, subject to bounded complexity; determining a new data point through optimal experimental design that informs best as for the underlying symbolic models; and updating a posterior distribution, given results of the experiment relating to the system under investigation for the determined new data point to enable informed assessment among a plurality of functional forms and parameterizations. An apparatus configured to perform the method is also provided.

Experimental design for symbolic model discovery

Techniques regarding topological classification of complex datasets are provided. For example, one or more embodiments described herein can comprise a system, which can comprise a memory that can store computer executable components. The system can also comprise a processor, operably coupled to the memory, and that can execute the computer executable components stored in the memory. The computer executable components can comprise a quantum computing component that can encode eigenvalues of a Laplacian matrix into a phase on a quantum state of a quantum circuit. The computer executable components can also comprise a classical computing component that infers a Betti number using a Bayesian learning algorithm by measuring an ancilla state of the quantum circuit.

Prior knowledge-based topological feature classification

A method of detecting cliques in a graph includes determining, based on a number of nodes in the graph, a number of qubits to be included in a quantum processor. The method includes assigning to each node in the graph, a qubit of the quantum processor. The method includes operating on the qubits with a preparation circuit to create a quantum state in the qubits that corresponds to the graph. The method includes operating on the quantum state with a random walk circuit, and measuring the qubits of the quantum processor to detect cliques in the graph. The preparation circuit comprises a plurality of single- and two-qubit operators, wherein, for each pair of adjacent nodes in the graph, an operator of the plurality of two-qubit operators acts on a pair of qubits corresponding to the pair of adjacent nodes to create the quantum state.

Quantum walk for community clique detection

A method is described for automatically correcting metadata errors in a k-mer database. A k-mer database having a self-consistent taxonomy based on genome-genome distance was constructed from a set of sample and reference genomes whose metadata included taxonomic labeling from a reference taxonomy (the standard NCBI taxonomy), which is not based on genetic distance. As a result, genomes of a given taxonomic ID of the self-consistent taxonomy could be separated into clusters based on the differences in the metadata. Genomes of the clusters less than a minimum cluster size Cmin were removed and profiled against the remaining genomes, correcting metadata automatically for those genomes that could be mapped back. The resulting k-mer database showed improved specificity for genetic profiling. Another method is described for identifying and handling chimeric genomes using the self-consistent taxonomy. Another method is described for correcting a classification database.

Methods of automatically and self-consistently correcting genome databases

A lower-dimensional representation (e.g., approximation) of a dataset is determined. The lower-dimensional representation can be used, for example, to perform semantic document analysis. Given a matrix of input data points, where each entry of the matrix indicates a number of times a particular term in a set of terms appears in a particular document in a set of documents, a lower-dimensional compressed matrix is obtained from the matrix by sampling rows of the matrix based on a target rank parameter, a desired accuracy tolerance, leverage scores calculated for the rows, and/or distances from rows of the matrix to a span of the initial set of sampled rows. The compressed matrix is used to determine a similarity metric indicative of a degree of similarity between documents. The documents can then be classified into a same document cluster or different clusters based on whether the similarity metric satisfied a threshold value.

Lower-dimensional subspace approximation of a dataset

One embodiment provides generating a similarity matrix corresponding to an input collection including initializing, by a processor, a working set as a collection of a multiple items. Until the similarity matrix converges: receiving a seed for similarity for at least one pair of items of the multiple items, and obtaining a similarity value for all other item pairs using a Naive Triangle Inequality process. The similarity is generated with obtained similarity values.

Efficient semi-supervised concept organization accelerated via an inequality process

A system for retrieving stored data includes memory and a processor. The memory stores a first matrix, A, having dimensions n&#xd7;d, a first sparse matrix, R, and a second sparse matrix, S. The processor receives an input value, k, corresponding to a selected rank to generate a second matrix, AR, by multiplying the first matrix, A, by the first sparse matrix, R. The second matrix, AT, has dimensions n&#xd7;t. The processor generates a third matrix, SA, by multiplying the second sparse matrix, S, by the first matrix, A. The third matrix, SA, has dimensions t'&#xd7;n, and the processor generates a fourth matrix, (SAR), by calculating a Moore-Penrose pseudo-inverse of a matrix, (SAR), and approximating the first matrix, A by generating a fifth matrix, &#xc3;, the fifth matrix defined as AR&#xd7;(SAR)&#xd7;SA.

Information retrieval using sparse matrix sketching

Embodiments of the invention relate to sketching for M-estimators for performing regression. One embodiment includes providing one or more sets of input data. A matrix A and a vector b are generated using the input data. A processor device is used for processing the matrix A and the vector b based on a randomized sketching matrix S. A vector x that minimizes a normalized measure function is determined based on the matrix A and the vector b. A relationship between the input data is determined based on the vector x.

Regression using M-estimators and polynomial kernel support vector machines and principal component regression

Growing community of inventors

Madison, NJ, United States of America

Kenneth Lee Clarkson