论文标题
使用小猪头近似值评估量子计算机上电子结构问题的各种汉密尔顿分区
Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation
论文作者
论文摘要
通过电子哈密顿量的单一演变解决电子结构问题是数字量子计算机的有前途应用之一。实施统一进化的实际策略之一是通过Trotterization，其中使用了一系列快速发展（即有效地对角线）的汉密尔顿碎片的短期演变。给定多种选择，将哈密顿分解为快速脱落的片段，哈密顿进化的准确性取决于片段的选择。我们使用费米和Qubit代数进行动作评估多个哈密顿分配技术的效率。使用电子哈密顿及其片段的对称性大大降低了猪肉误差。与基于Qubit的技术相比，这种降低使基于费米的分区践踏误差较低。但是，从模拟成本的角度来看，费米子方法倾向于在每个猪排步骤中引入更多T-gates数量的量子电路，因此与其量子相比，计算量更高。
Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via Trotterization, where a sequence of short-time evolutions of fast-forwardable (i.e. efficiently diagonalizable) Hamiltonian fragments is used. Given multiple choices of possible Hamiltonian decompositions to fast-forwardable fragments, the accuracy of the Hamiltonian evolution depends on the choice of the fragments. We assess efficiency of multiple Hamiltonian partitioning techniques using fermionic and qubit algebras for the Trotterization. Use of symmetries of the electronic Hamiltonian and its fragments significantly reduces the Trotter error. This reduction makes fermionic-based partitioning Trotter errors lower compared to those in qubit-based techniques. However, from the simulation-cost standpoint, fermionic methods tend to introduce quantum circuits with a greater number of T-gates at each Trotter step and thus are more computationally expensive compared to their qubit counterparts.
