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arXiv 2107.04019quant-phcond-mat.str-el
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利用量子泵实现原子团簇态的对称时间制备

Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps

Nathanan Tantivasadakarn, Ashvin Vishwanath

摘要:

最近已经确定,类簇状态-与簇状态处于相同的安全保护拓扑阶段的状态-提供了一系列可用于基于测量的量子计算的资源状态。在这项工作中,我们问是否有可能在有限的时间内准备集群状的状态,而不破坏对称性保护的资源状态。这样一个安全性保护协议将受益于拓扑保护的准备中的错误。我们回答这个问题的积极提供一个更高的维度,其有限时间的演化是一个单一的行为平凡的散装,但泵所需的集群状态的边界的哈密顿量。例子给出了由一个全球性的对称性保护的1D集群状态,和各种2D集群状态保护的子系统对称性。我们表明,即使不必要的对称扰动存在于驱动哈密顿量,投影测量的散装随着前馈校正是足够的恢复集群状的状态。

英文摘要:

It has recently been established that cluster-like states -- states that are in the same symmetry-protected topological phase as the cluster state -- provide a family of resource states that can be utilized for Measurement-Based Quantum Computation. In this work, we ask whether it is possible to prepare cluster-like states in finite time without breaking the symmetry protecting the resource state. Such a symmetry-preserving protocol would benefit from topological protection to errors in the preparation. We answer this question in the positive by providing a Hamiltonian in one higher dimension whose finite-time evolution is a unitary that acts trivially in the bulk, but pumps the desired cluster state to the boundary. Examples are given for both the 1D cluster state protected by a global symmetry, and various 2D cluster states protected by subsystem symmetries. We show that even if unwanted symmetric perturbations are present in the driving Hamiltonian, projective measurements in the bulk along with feedforward correction is sufficient to recover a cluster-like state.

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