论文标题
第二量量化的周期性固体的量子计算
Quantum Computation for Periodic Solids in Second Quantization
论文作者
论文摘要
在这项工作中，我们提出了一种量子算法，用于在错误校正的量子计算机上的周期性固体计算。该算法基于第二个量化的稀疏Qubitization方法，并为Bloch和Wannier基集开发。我们表明，对于BLOCH功能，Wannier功能需要较少的计算资源，因为：（i）可以利用Wannier功能的L $ _1 $规范较低，并且（ii）可以利用Wannier功能的翻译对称性，以减少必须加载到量子计算机中的经典数据的量。量子算法的资源需求估计了NIO和PDO等周期性固体。这些过渡金属氧化物在工业上与其催化特性有关。我们发现，使用200--900旋转轨道近似的汉密尔顿人的地面能量估计需要{\ it ca.}〜$ 10 {}^{10} $ - $ 10^{12} $ t gates $ t gates us，最高$ 3 \ cdot10^8 $物理Qubits的物理错误率为0.1 \％。
In this work, we present a quantum algorithm for ground-state energy calculations of periodic solids on error-corrected quantum computers. The algorithm is based on the sparse qubitization approach in second quantization and developed for Bloch and Wannier basis sets. We show that Wannier functions require less computational resources with respect to Bloch functions because: (i) the L$_1$ norm of the Hamiltonian is considerably lower and (ii) the translational symmetry of Wannier functions can be exploited in order to reduce the amount of classical data that must be loaded into the quantum computer. The resource requirements of the quantum algorithm are estimated for periodic solids such as NiO and PdO. These transition metal oxides are industrially relevant for their catalytic properties. We find that ground-state energy estimation of Hamiltonians approximated using 200--900 spin orbitals requires {\it ca.}~$10{}^{10}$--$10^{12}$ T gates and up to $3\cdot10^8$ physical qubits for a physical error rate of $0.1\%$.
