Abstract: A method to determine data uncertainty is provided. The method receives a high dimensional data input and a corresponding data output. The method trains a variational autoencoder (VAE) with the high dimensional data input to learn a low dimensional latent space representation of the high dimensional data input. An encoder part of the VAE outputs a set of distributions of the high dimensional dataset in a latent space. The method samples new data samples in the latent space using the set of distributions outputs from the encoder part of the VAE. The method learns a polynomial chaos expansion to map the new data samples in the latent space to the corresponding data output to learn the set of distributions and their relation to perform estimation with high-dimensional dataset under uncertainty such as missing values by estimating the values using the set of distributions.

Abstract: Techniques are provided to implement hardware accelerated application of preconditioners to solve linear equations. 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 entries of a preconditioning matrix which is storable in the array of cells. When the preconditioning matrix is stored in the array of cells, the processor is configured to apply the preconditioning matrix to a plurality of residual vectors by executing a process which includes performing analog matrix-vector multiplication operations on the preconditioning matrix and respective ones of the plurality of residual vectors to generate a plurality of output vectors used in one or more subsequent operations.

Abstract: An apparatus can include at least a controller, quantum hardware, and an interface. The controller can be configured to generate command signals. The quantum hardware can include at least a plurality of qubits. The interface can be connected to the controller and the quantum hardware, the interface being configured to control the quantum hardware based on the command signals to implement a quantum circuit configured to simulate a boundary operator that creates a mapping of boundaries of a given graph having nodes and edges. For example, the quantum circuit can be configured to simulate a boundary operator that creates a mapping of simplices of orders, e.g., of all orders, in a given simplicial complex. A method can include creating a boundary operator on a quantum computer, where a quantum circuit is built using Pauli spin operators.

Abstract: 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/(??))) where n is the number of data points, ? is the error tolerance, ? 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 ?.

Abstract: Systems and methods for operating quantum systems are described. A controller of a quantum system can generate a command signal. The quantum system can include quantum hardware having a plurality of qubits. An interface of the quantum system can control the quantum hardware based on the command signal to sample an input vector represented by the first set of qubits, where the input vector includes mixed states with different Hamming weights. The interface can control the quantum hardware to entangle the first set of qubits to the second set of qubits, where the second set of qubits represent a count of nonzero elements in the input vector. The interface can control the quantum hardware to generate an output vector based on the entanglement of the first set of qubits to the second set of qubits, where the output vector includes one or more states having a specific Hamming weight.

Abstract: Systems and methods for operating a quantum system are described. A controller of a quantum system can generate a command signal. The quantum system can include quantum hardware having a plurality of qubits. An interface of the quantum system can control the quantum hardware based on the command signal received from the controller to determine a plurality of moments of a matrix using a random state vector represented by the plurality of qubits. The controller can be further configured to output the plurality of moments of the matrix to a computing device to estimate a trace of a matrix function based on one or more selected moments among the plurality of moments. The matrix function can be a function of the matrix.

Abstract: Systems and methods for operating a quantum system are described. A controller of a quantum system can generate a command signal. The quantum system can include quantum hardware having a plurality of qubits. An interface of the quantum system can control the quantum hardware based on the command signal to generate a random state vector represented by the plurality of qubits. The random state vector can include a specific number of independent entries. The interface can control the quantum hardware to determine moments of a matrix based on the random state vector. The controller can be further configured to output the moments of the matrix to a computing device to estimate a trace of the matrix using the moments.

Abstract: Systems and methods for performing pairwise checking of data points in a dataset are described. An apparatus or computing device can include a controller, quantum hardware, and an interface. The controller can be configured to generate a command signal. The quantum hardware can include a plurality of qubits. The interface can be connected to the controller and the quantum hardware. The interface can be configured to control the quantum hardware based on the command signal received from the controller to perform pairwise checking for every pair of data points in a dataset to identify a property relating to the data points. The data points can be represented by the plurality of qubits.

Abstract: A system may receive a dynamic network graph and select an origination node. From the origination node, the system may deploy a random walk simulation on the dynamic network graph simulating steps from the origination node to one or more other nodes, and determine a convergence node for the random walk simulation.

Abstract: A computer implemented method for speeding up execution of a convex optimization operation one or more quadratic complexity operations to be performed by an analog crossbar hardware switch, and identifying one or more linear complexity operations to be performed by a CPU. At least one of the quadratic complexity operations is performed by the analog crossbar hardware, and at least one of the linear complexity operations is performed by the CPU. An iteration of an approximation of a solution to the convex optimization operation is updated by the CPU.

Abstract: Techniques are provided to implement hardware accelerated application of preconditioners to solve linear equations. 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 entries of a preconditioning matrix which is storable in the array of cells. When the preconditioning matrix is stored in the array of cells, the processor is configured to apply the preconditioning matrix to a plurality of residual vectors by executing a process which includes performing analog matrix-vector multiplication operations on the preconditioning matrix and respective ones of the plurality of residual vectors to generate a plurality of output vectors used in one or more subsequent operations.

Abstract: 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.

Abstract: 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.

Abstract: A computer-implemented method is presented for performing matrix sketching by employing an analog crossbar architecture. The method includes low rank updating a first matrix for a first period of time, copying the first matrix into a dynamic correction computing device, switching to a second matrix to low rank update the second matrix for a second period of time, as the second matrix is low rank updated, feeding the first matrix with first stochastic pulses to reset the first matrix back to a first matrix symmetry point, copying the second matrix into the dynamic correction computing device, switching back to the first matrix to low rank update the first matrix for a third period of time, and as the first matrix is low rank updated, feeding the second matrix with second stochastic pulses to reset the second matrix back to a second matrix symmetry point.

Abstract: 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.

Abstract: 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.

Abstract: Techniques for determining a count of triangles (tr) in a graph data structure using a crosspoint array is described. An adjacency matrix (a) representing the graph is mapped to the crosspoint array by configuring resistance values of crosspoint devices in the array. The count of triangles is initialized to zero (tr=0), and iteratively updated. The updating includes generating a first vector (x1) stochastically to include digital values in a predetermined range, which are converted into the voltage values. A multiplication of the adjacency matrix and the first vector (ax1) is computed using the crosspoint array. A second voltage vector (z1=ax1) is generated that includes voltage values representing the multiplication result. The adjacency matrix and the second voltage vector (z2=az1) are multiplied using the crosspoint array. The computer updates the number of triangles in the graph data structure as tr=tr+Z1T.

Abstract: A computer-implemented method for analyzing a time-varying graph is provided. The time-varying graph includes nodes representing elements in a network, edges representing transactions between elements, and data associated with the nodes and the edges. The computer-implemented method includes constructing, using a processor, adjacency and feature matrices describing each node and edge of each time-varying graph for stacking into an adjacency tensor and describing the data of each time-varying graph for stacking into a feature tensor, respectively. The adjacency and feature tensors are partitioned into adjacency and feature training tensors and into adjacency and feature validation tensors, respectively. An embedding model and a prediction model are created using the adjacency and feature training tensors. The embedding and prediction models are validated using the adjacency and feature validation tensors to identify an optimized embedding-prediction model pair.

Abstract: A computer-implemented method for automatic multilabel classification includes receiving a label matrix Y for multiple training instances. The label matrix Y includes multiple labels, each label representing a respective category. The method further includes computing an intermediate matrix YYT, where YT is a transpose of the label matrix Y. The method further includes computing a basis matrix H by a non-negative matrix factorization of the intermediate matrix YYT. The method further includes generating a group testing matrix A by sampling the basis matrix H. The method further includes generating, for each training instance from the training instances, a reduced label vector z by computing a product of the group testing matrix A and a label vector y for respective training instance from the label matrix Y. The method further includes predicting multiple labels associated with an input based on the reduced label vector z.

Abstract: 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.