Abstract: The present disclosure provides methods for computing first-order derivative properties of observables of fermionic systems, such as the derivatives of electronic ground and exited states of molecules and materials with respect to the positions of the nuclei, with the help of a quantum computer. The method has the advantageous property that first-order derivative properties with respect to an arbitrary number of parameters of the fermionic system can be computed with a quantum computational effort that is independent of the number of such parameters.

Abstract: The present disclosure is related to computational methods of determining intrinsic reaction coordinates (IRCs) for chemical transformations (e.g., chemical reactions) via dual nested integration.

Abstract: A method for preparing states on a quantum computer with given particle number and total spin squared quantum numbers by means of parametrized gates. Explicit decompositions of these gates are given for an embodiment of the method where fermions are mapped to the computational units of the quantum computer by means of a Jordan-Wigner mapping. As an example, the method is advantageous for the variational optimization of energies of chemical systems and the quantum computation of activation energies of chemical reactions.

Abstract: The disclosure is in the technical field of circuit-model quantum computation. Generally, it concerns methods to use quantum computers to perform computations on classical spin models, where the classical spin models involve a number of spins that is exponential in the number of qubits that comprise the quantum computer. Examples of such computations include optimization and calculation of thermal properties, but extend to a wide variety of calculations that can be performed using the configuration of a spin model with an exponential number of spins. Spin models encompass optimization problems, physics simulations, and neural networks (there is a correspondence between a single spin and a single neuron). This disclosure has applications in these three areas as well as any other area in which a spin model can be used.

Abstract: The disclosure is in the technical field of circuit-model quantum computation. Generally, it concerns methods to use quantum computers to perform computations on classical spin models, where the classical spin models involve a number of spins that is exponential in the number of qubits that comprise the quantum computer. Examples of such computations include optimization and calculation of thermal properties, but extend to a wide variety of calculations that can be performed using the configuration of a spin model with an exponential number of spins. Spin models encompass optimization problems, physics simulations, and neural networks (there is a correspondence between a single spin and a single neuron). This disclosure has applications in these three areas as well as any other area in which a spin model can be used.