标题： 量子电路和波包动力学的映射算法：质子化水簇和氢氧化物水簇中非简谐氢键的案例研究 显示英文标题

标题： Quantum circuit and mapping algorithms for wavepacket dynamics: case study of anharmonic hydrogen bonds in protonated and hydroxide water clusters

摘要： 精确计算波包核动力学被认为是一个经典上难以解决的问题，特别是随着维度的增加。 在这里，我们提出了两种算法，与我们开发的其他方法结合使用，将作为在任意维度上进行量子核动力学的基础。 对于其中一种算法，我们给出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状态动力学的自旋晶格哈密顿量之间的直接映射关系。 这种映射对三个量子比特来说是精确的，并且当其实现时，自旋态的动力学模拟了核波包的动力学。 然而，随着量子比特数量的增加，这种映射变得近似。 在第二种算法中，我们使用一种称为量子香农分解的方法，提出了一种针对此类问题的一般量子电路分解形式。 该算法更稳健，并且对于任意数量的量子比特都是精确的，代价是电路复杂度增加。 所得电路在IBM的量子仿真器（QASM）上实现了3到7个量子比特。 在这两种情况下，波包动力学与经典结果一致，从波包密度时间演化获得的相应振动频率，在几分之一波数范围内一致。 显示英文摘要

摘要： 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.