论文标题
降低单位线性组合的分子电子哈密顿模拟成本
Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
论文作者
论文摘要
我们考虑了分子电子结构汉密尔顿分子分解的不同线性组合（LCU）分解。在量子计算机上使用这些LCU分解进行哈密顿模拟，优点的主要图是其系数的1符号，这与量子电路复杂性有关。得出的是，给定的哈密顿量最低的LCU 1-符号是其光谱范围的一半。对于哈密顿将军而言，这种最低的规范分解实际上是无法实现的。因此，提出和评估了多种实用技术来产生LCU分解。还引入了使用对称性来进一步减少1符号的技术。除了在Schrödinger图片中考虑LCU外，我们还将其扩展到相互作用图片，从而大大降低了1个符号。
We consider different Linear Combination of Unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. Using these LCU decompositions for Hamiltonian simulation on a quantum computer, the main figure of merit is the 1-norm of their coefficients, which is associated with the quantum circuit complexity. It is derived that the lowest possible LCU 1-norm for a given Hamiltonian is half of its spectral range. This lowest norm decomposition is practically unattainable for general Hamiltonians; therefore, multiple practical techniques to generate LCU decompositions are proposed and assessed. A technique using symmetries to reduce the 1-norm further is also introduced. In addition to considering LCU in the Schrödinger picture, we extend it to the interaction picture, which substantially further reduces the 1-norm.
