International Business Machines Corporation

Tel Aviv University

Mark Steven Squillante

Lior Horesh

Vasileios Kalantzis

Kenneth Lee Clarkson

Wilfried Haensch

Tayfun Gokmen

Joseph L Hellerstein

Tomasz J Nowicki

Ismail Yunus Akhalwaya

Shashanka Ubaru

Tal Kachman

Li Feng Zhang

Zhen Liu

Chai Wah Wu

Liana Liyow Fong

Malte Johannes Rasch

Oguzhan Murat Onen

Honghui Xia

Jayram S Thathachar

Shun-Zheng Yu

John A Gunnels

Joel Leonard Wolf

Daniel Manuel Dias

Joseph Phillip Bigus

Nagui Halim

Soumyadip Ghosh

Richard Pervin King

Ajei Sarat Gopal

Haim Avron

Nayeem Islam

W Nathaniel Mills, Iii

Yingdong Lu

Antonius B Dieker

Andreas Leonidas Prodromidis

LeRoy Albert Krueger, Jr

Philip Shi-lung Yu

Charu Chandra Aggarwal

Philip Shilung Yu

Jayant R Kalagnanam

Ramasuri Narayanam

Jianying Hu

Bo Zhang

Aleksandra Mojsilovic

Roger E Hough

Dinesh Garg

Giacomo Nannicini

Mayank Sharma

Sujay Sunil Parekh

Aswin Kannan

Ana Radovanovic

Srirama Mandyam Krishnakumar

Xiaoxuan Zhang

Donald Allen Schlosnagle

Kazutoshi Yamazaki

Dmitriy A Katz-Rogozhnikov

Jeffrey Robert Pilgrim

Christian Toft-Nielsen

Jessica Lee Yau

Aditya Basu

Alankar Jain

Willy W Chiu

Jayachandran Sethuraman

Jeanine C Chong

Ogunzhan Murat Onen

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 are provided to implement hardware accelerated computing of eigenpairs of a matrix. For example, a system includes a processor, and a resistive processing unit coupled to the processor. The resistive processing unit includes an array of cells which include respective resistive devices, wherein at least a portion of the resistive devices are tunable to encode values of a given matrix which is storable in the array of cells. When the given matrix is stored in the array of cells, the processor is configured to determine an eigenvector of the stored matrix by executing a process which includes performing analog matrix-vector multiplication operations on the stored matrix to converge an initial vector to an estimate of the eigenvector of the stored matrix.

Hardware acceleration for computing eigenpairs of a matrix

A method is presented for computing an equilibrium distribution of Markov processes. The method includes storing weight values in an analog crossbar array of transition probability matrices, where the analog crossbar array of transition probability matrices represents a weight matrix with m rows and n columns, computing an eigenvector associated with a real eigenvalue of modulus one for each of the transition probability matrices, applying a gradient-based eigenvalue solver to converge to a dominant eigenpair, and determining a probability of changing from one state to another state in a stochastic entity based on outcomes of the gradient-based eigenvalue solver.

Markov processes using analog crossbar arrays

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 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

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

Methods and systems for solving a linear system include setting resistances in an array of settable electrical resistances in accordance with values of an input matrix. A series of input vectors is applied to the array as voltages to generate a series of respective output vectors. Each input vector in the series of vectors is updated based on comparison of the respective output vectors to a target vector. A solution of a linear system is determined that includes the input matrix based on the updated input vectors.

Analog hardware matrix computation

A method of performing Principal Component Analysis is provided. The method includes receiving, by a computing device, evolving data for processing/visualization. The method further includes, by the computing device, a dimensionality for reducing of the evolving data using the PCA, wherein the PCA is performed on analog crossbar hardware. The method also includes using, by the computing device, the evolving data for visualization having the dimensionality thereof reduced by the principal component analysis for a further application.

Fast PCA of evolving data using analog crossbar array

Methods and systems of evaluating a performance of an entity are described. A processor may obtain first data indicating tier attributes of resources of the entity, second data indicating function attributes of the resources, and third data indicating productivity attributes of the resources. The processor may train a model based on the first data, the second data, and the third data, the model may represent transitions of the resources over time. The processor may receive a set of controls including at least an objective to optimize a performance of the entity. The processor may generate a controlled model by integrating the set of controls into the model. The processor may determine a set of outcomes from the controlled model that includes at least a set of transitions relating to the resources that may optimize the performance of the entity.

Performance evaluation based on resource dynamics

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, computer system, and a computer program product for computing a product drag effect is provided. The present invention may include receiving a plurality of transaction record data. The present invention may then include tuning a plurality of parameters based on the received transaction record data. The present invention may further include determining a product drag frequency based on the authorized parameter tuning and received transaction record data. The present invention may then include calculating a drag probability based on the determined product drag frequency. The present invention may then include deriving an observation from the calculated drag probability. The present invention may lastly include outputting the derived observation to a user.

Extracting product drag effect from transaction records

A computer-implemented method for Eigenpair computation is provided. The method includes computing, her a hardware processor, an Eigenvector and respective Eigenvalues of the Eigenvector of a matrix by using a modified Stochastic Optimization process including performing a matrix vector product on a Resistive Processing Unit (RPU) crossbar array operatively coupled to the hardware processor and performing a scalar vector product on a digital device operatively coupled to the hardware processor and representing, for each of an Eigenpair, an initial guess for the Eigenvector and the respective Eigenvalues. The computing step includes storing the matrix in the RPU crossbar array.

Eigenvalue decomposition with stochastic optimization

A system, method and computer program product for managing capacities and structures in a stochastic network. The method includes mapping the stochastic network to a general analytic model, e.g., a Brownian model, decomposing the general analytic model of the stochastic network into a set of smaller general analytic models, determining the capacities/structures for the set of analytic models as an intermediate solution for the capacities/structures of the stochastic network; and, determining the capacities/structures for the stochastic network starting at the intermediate solution for the capacities/structures using simulation-based methods.

Managing capacities and structures in stochastic networks

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Pound Ridge, NY, United States of America

Mark Steven Squillante