论文标题
在嘈杂的中间量子计算机上准备价值 - 债券状态
Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
论文作者
论文摘要
量子状态制备是所有数字量子模拟算法中的关键步骤。在这里，我们提出的方法是在基于门的量子计算机上初始化一般的量子自旋波函数（所谓的价键 - 固体（VBS）状态）的一般类别，这对于有两个原因很重要。首先，VBS状态是Affleck，Kennedy，Lieb和Tasaki（AKLT）引入的一类相互作用量子自旋模型的确切基态。其次，二维VBS状态是用于基于测量的量子计算的通用资源状态。我们发现，基于其张量 - 网络表示形式制备VBS状态的方案产生的量子电路太深，无法触及嘈杂的中等规模量子（NISQ）计算机。然后，我们在本文提出的一般非确定性方法中应用Spin-1和Spin-3/2 VBS状态的制备，即分别在一个维度和蜂窝晶格中定义的AKLT模型的基态。对于两种情况，深度与晶格大小无关的浅量子电路都明确得出，利用优于标准基础门分解方法的优化方案。鉴于所提出的例程的概率性质，设计了两种二次减少重复开销的策略，用于在两部分晶格上定义的任何VBS状态。我们的方法应允许使用NISQ处理器来探索AKLT模型和变体，在不久的将来超过常规数值方法。
Quantum state preparation is a key step in all digital quantum simulation algorithms. Here we propose methods to initialize on a gate-based quantum computer a general class of quantum spin wave functions, the so-called Valence-Bond-Solid (VBS) states, that are important for two reasons. First, VBS states are the exact ground states of a class of interacting quantum spin models introduced by Affleck, Kennedy, Lieb and Tasaki (AKLT). Second, the two-dimensional VBS states are universal resource states for measurement-based quantum computing. We find that schemes to prepare VBS states based on their tensor-network representations yield quantum circuits that are too deep to be within reach of noisy intermediate-scale quantum (NISQ) computers. We then apply the general non-deterministic method herein proposed to the preparation of the spin-1 and spin-3/2 VBS states, the ground states of the AKLT models defined in one dimension and in the honeycomb lattice, respectively. Shallow quantum circuits of depth independent of the lattice size are explicitly derived for both cases, making use of optimization schemes that outperform standard basis gate decomposition methods. Given the probabilistic nature of the proposed routine, two strategies that achieve a quadratic reduction of the repetition overhead for any VBS state defined on a bipartite lattice are devised. Our approach should permit to use NISQ processors to explore the AKLT model and variants thereof, outperforming conventional numerical methods in the near future.
