Search for: All records

The accurate computational study of wavepacketnuclear dynamics is considered to be a classically intractableproblem, particularly with increasing dimensions. Here, we presenttwo algorithms that, in conjunction with other methods developedby us, may result in one set of contributions for performingquantum nuclear dynamics in arbitrary dimensions. For one of thetwo algorithms discussed here, we present a direct map betweenthe Born−Oppenheimer Hamiltonian describing the nuclearwavepacket time evolution and the control parameters of a spin−lattice Hamiltonian that describes the dynamics of qubit states in anion-trap quantum computer. This map is exact for three qubits, andwhen implemented, the dynamics of the spin states emulates thoseof the nuclear wavepacket in a continuous representation. However, this map becomes approximate as the number of qubits grows.In a second algorithm, we present a general quantum circuit decomposition formalism for such problems using a method called theQuantum Shannon Decomposition. This algorithm is more robust and is exact for any number of qubits at the cost of increasedcircuit complexity. The resultant circuit is implemented on IBM’s quantum simulator (QASM) for 3−7 qubits, without using a noisemodel so as to test the intrinsic accuracy of the method. In both cases, the wavepacket dynamics is found to be in good agreementwith the classical propagation result and the corresponding vibrational frequencies obtained from the wavepacket density timeevolution are in agreement to within a few tenths of a wavenumber. 

The exponential scaling of the quantum degrees of freedom with the size of the system is one of the biggest challenges in computational chemistry and particularly in quantum dynamics. We present a tensor network approach for the time-evolution of the nuclear degrees of freedom of multiconfigurational chemical systems at a reduced storage and computational complexity. We also present quantum algorithms for the resultant dynamics. To preserve the compression advantage achieved via tensor network decompositions, we present an adaptive algorithm for the regularization of nonphysical bond dimensions, preventing the potentially exponential growth of these with time. While applicable to any quantum dynamical problem, our method is particularly valuable for dynamical simulations of nuclear chemical systems. Our algorithm is demonstrated using ab initio potentials obtained for a symmetric hydrogen-bonded system, namely, the protonated 2,2′-bipyridine, and compared to exact diagonalization numerical results. 

We provide an approach to sample rare events during classical ab initio molecular dynamics and quantum wavepacket dynamics. For classical AIMD, a set of fictitious degrees of freedom are introduced that may harmonically interact with the electronic and nuclear degrees of freedom to steer the dynamics in a conservative fashion toward energetically forbidden regions. A similar approach when introduced for quantum wavepacket dynamics has the effect of biasing the trajectory of the wavepacket centroid toward the regions of the potential surface that are difficult to sample. The approach is demonstrated for a phenol-amine system, which is a prototypical problem for condensed phase-proton transfer, and for model potentials undergoing wavepacket dynamics. In all cases, the approach yields trajectories that conserve energy while sampling rare events. 

We present a graph-theory-based reformulation of all ONIOM-based molecular fragmentation methods. We discuss applications to (a) accurate post-Hartree–Fock AIMD that can be conducted at DFT cost for medium-sized systems, (b) hybrid DFT condensed-phase studies at the cost of pure density functionals, (c) reduced cost on-the-fly large basis gas-phase AIMD and condensed-phase studies, (d) post-Hartree–Fock-level potential surfaces at DFT cost to obtain quantum nuclear effects, and (e) novel transfer machine learning protocols derived from these measures. Additionally, in previous work, the unifying strategy discussed here has been used to construct new quantum computing algorithms. Thus, we conclude that this reformulation is robust and accurate.