论文标题
估计费米尼真空隔离准备的栅极复杂性
Estimating gate complexities for the site-by-site preparation of fermionic vacua
论文作者
论文摘要
量子模拟的一个重要方面是在量子计算机上准备身体上有趣的状态，并且该任务通常可能是昂贵或具有挑战性的。在Arxiv：1911.03505中引入了一种数字状态准备的数字``现场准备方案''，作为一种用质量差距制备某些费米子田间理论的真空状态的一种方式。更一般而言，只要连续的中间基态具有非零重叠，并且哈密顿量在有限的晶状体大小的情况下，该算法可用于准备汉密尔顿人的基础状态。在本文中，我们研究了基态重叠，这是一系列二次费米子汉密尔顿人的地点数量的函数。使用以免费费米为名的分析公式，我们能够探索较大的$ n $行为并得出有关国家重叠的结论。对于所有研究的型号，我们发现重叠仍然很大（例如$> 0.1 $），直至大晶格尺寸（$ n = 64,72 $），除了近量子相变或存在间隙边缘模式。对于一维系统，我们进一步发现，两个$ n/2 $的基础状态也与$ n $ n $点的地下状态共享大量重叠，除了相位边界附近的一个区域。基于这些数值结果，我们还提出了逐个位置状态制备算法的递归替代方法。
An important aspect of quantum simulation is the preparation of physically interesting states on a quantum computer, and this task can often be costly or challenging to implement. A digital, ``site-by-site'' scheme of state preparation was introduced in arXiv:1911.03505 as a way to prepare the vacuum state of certain fermionic field theory Hamiltonians with a mass gap. More generally, this algorithm may be used to prepare ground states of Hamiltonians by adding one site at a time as long as successive intermediate ground states share a non-zero overlap and the Hamiltonian has a non-vanishing spectral gap at finite lattice size. In this paper, we study the ground state overlap as a function of the number of sites for a range of quadratic fermionic Hamiltonians. Using analytical formulas known for free fermions, we are able to explore the large-$N$ behavior and draw conclusions about the state overlap. For all models studied, we find that the overlap remains large (e.g. $> 0.1$) up to large lattice sizes ($N=64,72$) except near quantum phase transitions or in the presence of gapless edge modes. For one-dimensional systems, we further find that two $N/2$-site ground states also share a large overlap with the $N$-site ground state everywhere except a region near the phase boundary. Based on these numerical results, we additionally propose a recursive alternative to the site-by-site state preparation algorithm.
