论文标题
相关电子材料中哈密顿模拟的资源估计
Resource estimations for the Hamiltonian simulation in correlated electron materials
论文作者
论文摘要
相关的电子材料(例如超导体和磁性材料)被认为是量子计算中引人入胜的目标。但是,执行量子算法以模拟相关电子材料所需的定量资源,特别是量子门和量子位的数量,尚不清楚。在这项研究中,我们估算了使用费米子掉期网络的相关电子材料,专门针对有机超导体,基于铁的超导体,二元过渡金属氧化物和钙钛矿氧化物所需的资源。使用$ ab〜1ain $ downdlolding方法得出的有效的哈密顿式化方法,用于哈密顿模拟,并提出了通过使用费米昂交换网络为有效的哈密顿人(包括交换互动)的费米子交换网络进行资源估算的程序。例如,在系统中的$ 10^2 $单元单元中,平均相关的电子材料平均而言,平均每个小铲式步骤和Qubits的门数分别为$ 10^7 $和$ 10^3 $。此外,我们的结果表明,当构成整个系统的单位单元格的数量高达$ 10^2 $时,有效的哈密顿量中的相互作用项数量,尤其是对于库仑的交互项,在栅极资源中是主要的,而当单位单元的数量更多时,费尔米式交换操作的数量主要是$ 10^3 $。
Correlated electron materials, such as superconductors and magnetic materials, are regarded as fascinating targets in quantum computing. However, the quantitative resources, specifically the number of quantum gates and qubits, required to perform a quantum algorithm to simulate correlated electron materials remain unclear. In this study, we estimate the resources required for the Hamiltonian simulation algorithm for correlated electron materials, specifically for organic superconductors, iron-based superconductors, binary transition metal oxides, and perovskite oxides, using the fermionic swap network. The effective Hamiltonian derived using the $ab~initio$ downfolding method is adopted for the Hamiltonian simulation, and a procedure for the resource estimation by using the fermionic swap network for the effective Hamiltonians including the exchange interactions is proposed. For example, in the system for the $10^2$ unit cells, the estimated number of gates per Trotter step and qubits are approximately $10^7$ and $10^3$, respectively, on average for the correlated electron materials. Furthermore, our results show that the number of interaction terms in the effective Hamiltonian, especially for the Coulomb interaction terms, is dominant in the gate resources when the number of unit cells constituting the whole system is up to $10^2$, whereas the number of fermionic swap operations is dominant when the number of unit cells is more than $10^3$.