The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here we present two algorithms that, in conjunction with other methods developed by us, will form the basis for performing quantum nuclear dynamics in arbitrary dimensions. For one algorithm, we present a direct map between the Born-Oppenheimer Hamiltonian describing the wavepacket time-evolution and the control parameters of a spin-lattice Hamiltonian that describes the dynamics of qubit states in an ion-trap quantum computer. This map is exact for three qubits, and when implemented, the dynamics of the spin states emulate those of the nuclear wavepacket. However, this map becomes approximate as the number of qubits grow. In a second algorithm we present a general quantum circuit decomposition formalism for such problems using a method called the Quantum Shannon Decomposition. This algorithm is more robust and is exact for any number of qubits, at the cost of increased circuit complexity. The resultant circuit is implemented on IBM's quantum simulator (QASM) for 3-7 qubits. In both cases the wavepacket dynamics is found to be in good agreement with the classical result and the corresponding vibrational frequencies obtained from the wavepacket density time-evolution, are in agreement to within a few tenths of a wavenumbers.

翻译：波包核动力学的精确计算研究被视为一类经典难解问题，尤其随着维度增加而愈发困难。本文提出两种算法，结合我们开发的其他方法，将构成在任意维度执行量子核动力学的基础。对于第一种算法，我们建立了描述波包时间演化的玻恩-奥本海默哈密顿量与描述离子阱量子计算机中量子比特态动力学的自旋晶格哈密顿量控制参数之间的直接映射。该映射对三个量子比特是精确的，实际执行时自旋态的动力学行为可模拟核波包动力学。然而随着量子比特数增加，该映射会变为近似。在第二种算法中，我们利用称为量子香农分解的方法，为此类问题提出通用的量子电路分解形式。该算法更具鲁棒性，且对任意数量量子比特均保持精确性，代价是电路复杂度增加。所得电路在IBM量子模拟器（QASM）上针对3-7个量子比特实现。两种方法得到的波包动力学均与经典结果高度吻合，从波包密度时间演化获得的相应振动频率差异在几个波数十分之一范围内。