Abstract: A method for obtaining a refined model given a mis-specified symbolic model. The method includes receiving a mis-specified symbolic model and data pertaining to a process or phenomenon corresponding to the mis-specified symbolic model; receiving one or more constraints; generating a plurality of partial expression trees based on the mis-specified symbolic model; solving an optimization problem for each of the partial expression trees; and determining a refined symbolic model of the mis-specified symbolic model based on results of the optimization problem for each partial expression tree.

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: Embodiments of the invention are directed to a programmable computer system having a processor system operable to perform processor system operations that include representing a set of candidate functions in a mathematical expression domain. The set of candidate functions defines relationships between data of an existing system. A set of known background theory is represented in the mathematical expression domain. The set of known background theory defines known relationships associated with the existing system. A model composition operation is performed that includes analyzing, in the mathematical expression domain, the set of candidate functions and the set of known background theory to generate a composed model that satisfies a target data fidelity in a manner that also satisfies a predetermined level of compatibility between the composed model and the set of known background theory.

Abstract: A method generates automated discovery of new scientific formulas. The method includes receiving a background theory associated with a phenomenon being studied. The processor receives a set of training data associated with the phenomenon being studied. The set of training data is processed in a machine learning model that generates candidate formulas from data points in the set of training data. Values of a numerical error-vector are generated for the candidate formulas. The candidate formulas are processed in a reasoning model. The operation of the reasoning model includes generating values of a theoretical error-vector based on the background theory. An output of a performance metric is generated based on a generalization of the theoretical error-vector and a reasoning error. The processor determines whether one of the candidate formulas is a meaningful and valid new scientific formula, based on a behavior of the reasoning error and the reasoning performance metric.

Abstract: 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.

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 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: 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 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, 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.

Abstract: 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.

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: Methods and systems for performing a natural language processing task include identifying hypernym/hyponym relations in a depth-wise ontology and identifying synonymy relations in a breadth-wise ontology. The depth-wise ontology and the breadth-wise ontology are combined into a combined ontology using the identified hypernym/hyponym relations and the identified synonymy relations. Enhanced hypernym/hyponym relations are embedded using the combined ontology. A natural language processing task is performed using the enhanced hypernym/hyponym relations and the combined ontology.

Abstract: 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.

Abstract: 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.

Abstract: 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.