Quantum simulations of electronic structure with a transformed Hamiltonian that includes some electron correlation effects are demonstrated. The transcorrelated Hamiltonian used in this work is efficiently constructed classically, at polynomial...
Quantum chemistry simulations of some industrially relevant molecules are reported, employing variational quantum algorithms for near-term quantum devices. The energies and dipole moments are calculated along the dissociation curves for lithium hydride (LiH), hydrogen sulfide, lithium hydrogen sulfide, and lithium sulfide. In all cases, we focus on the breaking of a single bond to obtain information about the stability of the molecular species being investigated. We calculate energies and a variety of electrostatic properties of these molecules using classical simulators of quantum devices, with up to 21 qubits for lithium sulfide. Moreover, we calculate the ground-state energy and dipole moment along the dissociation pathway of LiH using IBM quantum devices. This is the first example, to the best of our knowledge, of dipole moment calculations being performed on quantum hardware.
Dengue viral infections show unique infection patterns arising from its four serotypes, 2,3,4). Its effects range from simple fever in primary infections to potentially fatal secondary infections. We analytically and numerically analyse virus dynamics and humoral response in a host during primary and secondary dengue infection for long periods using micro-epidemic models. The models presented here incorporate time delays, antibody dependent enhancement (ADE), a dynamic switch and a correlation factor between different DENV serotypes. We find that the viral load goes down to undetectable levels within 7-14 days as is observed for dengue infection, in both cases. For primary infection, the stability analysis of steady states shows interesting dependence on the time delay involved in the production of antibodies from plasma cells. We demonstrate the existence of a critical value for the immune response parameter, beyond which the infection gets completely cured. For secondary infections with a different serotype, the homologous antibody production is enhanced due to the influence of heterologous antibodies. The antibody production is also controlled by the correlation factor, which is a measure of similarities between the different DENV serotypes involved. Our results agree with clinically observed humoral responses for primary and secondary infections.
Currently available noisy intermediate-scale quantum (NISQ) devices are limited by the number of qubits that can be used for quantum chemistry calculations on molecules. We show herein that the number of qubits required for simulations on a quantum computer can be reduced by limiting the number of orbitals in the active space. Thus, we have utilized ansätze that approximate exact classical matrix eigenvalue decomposition methods (Full Configuration Interaction). Such methods are appropriate for computations with the Variational Quantum Eigensolver algorithm to perform computational investigations on the rearrangement of the lithium superoxide dimer with both quantum simulators and quantum devices. These results demonstrate that, even with a limited orbital active space, quantum simulators are capable of obtaining energy values that are similar to the exact ones. However, calculations on quantum hardware underestimate energies even after the application of readout error mitigation.
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. It can be shown quantum kernels exist that, subject to computational hardness assumptions, can not be computed classically. It is an important challenge to find quantum kernels that provide an advantage in the classification of real world data. Here we introduce a class of quantum kernels that are related to covariant quantum measurements and can be used for data that has a group structure. The kernel is defined in terms of a single fiducial state that can be optimized by using a technique called kernel alignment. Quantum kernel alignment optimizes the kernel family to minimize the upper bound on the generalisation error for a given data set. We apply this general method to a specific learning problem we refer to as labeling cosets with error and implement the learning algorithm on 27 qubits of a superconducting processor.
The computational description of correlated electronic structure, and particularly of excited states of many-electron systems, is an anticipated application for quantum devices. An important ramification is to determine the dominant molecular fragmentation pathways in...
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