论文标题
费尔米金汉密尔顿人的选择（H）的实现速度更快
Exponentially faster implementations of Select(H) for fermionic Hamiltonians
论文作者
论文摘要
我们提出了一个简单但一般的框架，用于构建量子循环，该量子循环可以实现多个统一的$ \ text {select}（h）费米金哈密顿。 $ \ text {select}（h）$是几种量子算法的主要子例程之一，包括用于哈密顿模拟的最新技术。如果在第二量化的哈密顿量中的每个术语最多涉及$ k $旋转轨道和$ k $是一个不变的是独立于旋转轨道$ n $的总数（与大多数量子化学和凝结的物质模型一样$ \ mathcal {o}（n）$ clifford+t门，clifford门在$ \ mathcal {o}中应用了（\ log^2 n）$ layers，而$ t $ Gates in $ o（\ log n）$ layers中的$ t $ gates。这在维持线性门计数并将附件的数量减少到零的同时，在以前的工作中取得了指数改善。
We present a simple but general framework for constructing quantum circuits that implement the multiply-controlled unitary $\text{Select}(H) \equiv \sum_\ell |\ell\rangle\langle\ell|\otimes H_\ell$, where $H = \sum_\ell H_\ell$ is the Jordan-Wigner transform of an arbitrary second-quantised fermionic Hamiltonian. $\text{Select}(H)$ is one of the main subroutines of several quantum algorithms, including state-of-the-art techniques for Hamiltonian simulation. If each term in the second-quantised Hamiltonian involves at most $k$ spin-orbitals and $k$ is a constant independent of the total number of spin-orbitals $n$ (as is the case for the majority of quantum chemistry and condensed matter models considered in the literature, for which $k$ is typically 2 or 4), our implementation of $\text{Select}(H)$ requires no ancilla qubits and uses $\mathcal{O}(n)$ Clifford+T gates, with the Clifford gates applied in $\mathcal{O}(\log^2 n)$ layers and the $T$ gates in $O(\log n)$ layers. This achieves an exponential improvement in both Clifford- and T-depth over previous work, while maintaining linear gate count and reducing the number of ancillae to zero.
