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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. 

We describe a general formalism for quantum dynamics and show how this formalism subsumes several quantum algorithms including the Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Shor algorithms as well as the conventional approach to quantum dynamics based on tensor networks. The common framework exposes similarities among quantum algorithms and natural quantum phenomena: we illustrate this connection by showing how the correlated behavior of protons in water wire systems that are common in many biological and materials systems parallels the structure of Shor's algorithm.