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: Using a hardware processor, load a matrix. Compute, using the hardware processor, diagonal entry approximations for the matrix by using one or more probing vectors. Apply, using the hardware processor, an Aitken extrapolation to the diagonal entry approximations. Obtain, using the hardware processor, a final diagonal estimation based on the Aitken extrapolation. Optionally, the matrix comprises a matrix of material properties of a first material, and further actions include, based on the final diagonal estimation for the first material, determining that the first material is suitable for a certain application, based on the determination that the first material is suitable, specifying the first material; and, responsive to the specifying, using the hardware processor to control a machine tool to fabricate a part of the first material.

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: Solving linear systems by sending matrix data from a first computer to a second computer, directing the second computer in determining a solution to a parallel computing task for the matrix data, receiving the solution by the first computer, determining a solution to a non-parallel computing task for the matrix data using the first computer, and providing the solution to the non-parallel computing task.

Abstract: A directed graph autoencoder device includes one or more memories and a processor coupled to the one or more memories and configured to implement a graph convolutional layer. The graph convolutional layer comprises a plurality of nodes and is configured to generate transformed dual vector representations by applying a source weight matrix and a target weight matrix to input dual vector representations of the plurality of nodes. The input dual vector representations comprise, for each node of the plurality of nodes, a source vector representation that corresponds to the node in its role as a source and a target vector representation that corresponds to the node in its role as a target. The graph convolutional layer is further configured to scale the transformed dual vector representations to generate scaled transformed dual vector representations. The graph convolutional layer is further configured to perform message passing using the scaled transformed dual vector representations.

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 method of computation includes receiving, by a requesting device, a system of linear equations, and computing a solution to the system of linear equations by a flexible iterative algorithm. The computing includes, for each iteration, determining a most computationally expensive operation of the iteration, mapping the most expensive operation to a low precision format, performing the most expensive operation according to a low precision, performing other operations of the iteration according to a high precision, and returning the solution to the requesting device.

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: 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 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 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 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 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: A device solves for eigenvalues of a matrix system. The device performs a domain decomposition of a matrix system into non-overlapping subdomains and a reordering of matrices of the matrix system. An interface variable projection subspace associated with interface variables of an adjacency graph of the matrix system is created. The interface variables are related to nodes of the adjacency graph which are connected with nodes located in neighboring partitions. An internal variable projection subspace is created that is associated with internal variables of the adjacency graph of the matrix system, wherein the internal variables are related to nodes of the adjacency graph which are connected only to nodes located in the same partition. A projection matrix is built based on the interface variable projection subspace and the internal variable projection subspace. The device determines eigenvalues that solve a Raleigh-Ritz eigenvalue problem utilizing the projection matrix.

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 processor performing machine learning including spectral clustering can receive data from the sensor. Graph Laplacian of the data can be created and stored in a memory device. Spectral characteristic can be created by applying density of states and spectral gaps can be detected in an unsupervised manner in the spectral characteristic to determine r as number of clusters to cluster the data. A range space of a rational matrix of the graph Laplacian can be determined. K-means clustering can be performed on the range space of rational matrix of the graph Laplacian using r as the number of clusters, the K-means clustering returning r clusters of the received data.