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.

Abstract: 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.

Abstract: In an embodiment, a method of sketching using a hybrid quantum-classical system includes creating a set of clustered data sets from a first data set. In an embodiment, the method includes evaluating, using a quantum processor and quantum memory, the set of clustered data sets. In an embodiment, the method includes evaluating, using the quantum processor and quantum memory, a set of quality metrics for the set of clustered data sets. In an embodiment, the method includes reclustering, responsive to at least one of the set of quality metrics failing to meet a quality criterion, the first data set.

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 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.

Abstract: Hybrid classical-quantum decision maker training includes receiving a training data set, and selecting, by a first processor, a sampling of objects from the training set, each object represented by at least one vector. A quantum processor applies a quantum feature map to the selected objects to produce one or more output vectors. The first processor determines one or more distance measures between pairs of the output vectors, and determines at least one portion of the quantum feature map to modify the classical feature map. The first processor adds an implementation of the at least one portion of the quantum feature map to the classical feature map to generate an updated classical feature map.

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: In an embodiment, a method includes classifying, using a neural network including quantum components, a data set to generate a first set of classified data. In the embodiment, the method includes generating noise in the quantum components. In the embodiment, the method includes reclassifying, using the neural network, the data set with the generated noise to generate a second set of classified data. In the embodiment, the method includes determining, responsive to comparing the first set of classified data and the second set of classified data, a sensitivity of the quantum components.

Abstract: In an embodiment, a method of sketching using a hybrid quantum-classical system includes creating a set of clustered data sets from a first data set. In an embodiment, the method includes evaluating, using a quantum processor and quantum memory, the set of clustered data sets. In an embodiment, the method includes evaluating, using the quantum processor and quantum memory, a set of quality metrics for the set of clustered data sets. In an embodiment, the method includes reclustering, responsive to at least one of the set of quality metrics failing to meet a quality criterion, the first data set.

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: Hybrid classical-quantum decision maker training includes receiving a training data set, and selecting, by a first processor, a sampling of objects from the training set, each object represented by at least one vector. A quantum processor applies a quantum feature map to the selected objects to produce one or more output vectors. The first processor determines one or more distance measures between pairs of the output vectors, and determines at least one portion of the quantum feature map to modify the classical feature map. The first processor adds an implementation of the at least one portion of the quantum feature map to the classical feature map to generate an updated classical feature map.