Grover量子搜索算法在具有一次和二次近邻耦合的Ising核自旋链量子计算机中的模拟

单激发次近邻量子比特链的特征多项式

The characteristic polynomial of the next-nearest-neighbour qubit chain for single excitations

研究了具有最近邻和次最近邻相互作用的偶极-偶极耦合二能级原子链的单光子激发本征值和本征矢量的特征多项式。我们发现的确切形式的多项式的Chebyshev多项式的第二类，是有效的任意数量的原子和耦合强度。然后，我们提出了一种技术，用于表示多项式的根作为一个幂级数的耦合常数。的解决方案的一般性质也进行了探讨，以阐明的一般性质，确切的，解析形式的能量本征值应该有。还概述了一种方法用于推导本征向量的哈密顿量。

Shor算法在线性最近邻量子比特阵列上的实现

Implementation of Shor's Algorithm on a Linear Nearest Neighbour Qubit Array

Shor的算法，在适当的硬件条件下，可以将整数$N$分解为二进制长度为$L$的时间多项式，这无疑刺激了建造实用量子计算机的竞赛。已经设计了几种不同的实现肖尔算法的量子线路，但每一种都默认计算机内的任意量子比特对可以相互作用。虽然一些量子计算机架构具有这种特性，但许多有前途的建议最适合实现仅具有最近邻相互作用的单线量子位。鉴于此，我们提出了一种电路实现肖尔的因式分解算法设计的线性最近邻架构。尽管有相互作用的限制，该电路只需要$2L+4$量子位，一阶需要$8L^{4}$门安排在深度为$32L^{3}$的电路中-与一阶相同，使用可以相互作用任意量子位对的架构。

最近邻通信容错计算的门限错误惩罚

Threshold Error Penalty for Fault Tolerant Computation with Nearest Neighbour Communication

容错量子计算的错误阈值与量子比特的级联编码是由内部通信开销惩罚。许多量子计算方案依赖于最近邻通信，这需要额外的门操作。对于一个宽度为L+1个物理量子比特的量子比特条带，实现L级级联，我们发现，当门错误是主要的错误来源时，在没有任何通信负担的情况下，错误阈值从2.1x10^-5降低到1.2x10^-7。误差阈值的这一~ 175倍损失转化为门操作控制脉冲的幅度和定时的~ 13倍损失。

面向$K$近邻算法的量子光学方法

Quantum Optical Approach to the $K$ Nearest Neighbour Algorithm

本研究提出一种$K$近邻算法的量子-经典混合实现方法，借助单光子将信息嵌入多模相干态，由量子光学计算机计算相似度、经典计算机完成排序分类，优化了计算资源并在多类数据集上验证了应用价值。

Fast and robust quantum state transfer in a topological Su-Schrieffer-Heeger chain with Next-to-Nearest-Neighbour interactions

We suggest a method for fast and robust quantum-state transfer in a Su-Schrieffer-Heeger (SSH) chain, which exploits the use of next-to-nearest-neighbour (NNN) interactions. The proposed quantum protocol combines a rapid change in one of the topological edge states, induced by a modulation of nearest-neighbour interactions, with a fine tuning of NNN interactions operating a counter-adiabatic driving. The latter cancels nonadiabatic excitations from the edge state multiplicity to the energy bands. We use this shortcut technique for topological pumping of edge states on a single dimerized chain …

宏观二聚体系统的非对称性诱导纠缠

Dimensionality induced entanglement in macroscopic dimer systems

研究了任意拓扑和维数的晶格中短程自旋-s二聚体覆盖混合物的纠缠性质。我们证明了在一维空间中，任何自旋$s$都存在最近邻纠缠。令人惊讶的是，在更高的空间维度有一个阈值的自旋$s$低于最近邻纠缠消失。传统的“经典”极限的大自旋值对应的最高最近邻纠缠，我们量化使用的负值。

Recommendation systems with quantum k-NN and Grover's algorithms for data processing

In this article, we discuss the implementation of a quantum recommendation system that uses a quantum variant of the k-nearest neighbours algorithm and the Grover algorithm to search for a specific element in unstructured database. In addition to the presentation of the recommendation system as an algorithm, the article also shows a main steps in construction of a suitable quantum circuit for realisation of a given recommendation system. The computational complexity of individual calculation steps during recommendation system was also indicated. The verification correctness of a proposed recom…

Engineered Nearest-Neighbour Interactions with Doubly Modulated Optical Lattices

Optical lattice systems provide exceptional platforms for quantum simulation of many-body systems. We focus on the doubly modulated Bose-Hubbard model driven by both time-dependent on-site energy and interaction, and predict the emergence of the nearest neighbour interaction and density-assisted tunnelling. By specifically designing a bi-chromatic driving pattern for a one dimensional lattice, we demonstrate that the doubly modulated fields can be tuned to realize desired quantum phases, e.g. the Mott insulator phase with selective defects, and density wave phase.

具有近邻相互作用的旋转光晶格中的冷原子

Cold atoms in rotating optical lattice with nearest neighbour interaction

考虑最近邻相互作用的扩展Bose哈伯德模型最小限度地描述了长程相互作用对深光晶格中超冷原子的影响。这种光晶格的旋转使这种中性冷原子受到人工磁场的影响。这种旋转对密度波相界和莫特绝缘体相界的改变与旋量和标量Harper方程的边缘谱有关。计算了密度波相界附近具有亚格子调制超流序参量的棋盘格涡态的相应轮廓。

Quantization of β-Fermi-Pasta-Ulam Lattice with Nearest and Next-nearest Neighbour Interactions

We quantize the β-Fermi-Pasta-Ulam (FPU) model with nearest and next-nearest neighbour interactions using a number conserving approximation and a numerical exact diagonalization method. Our numerical mean field bi-phonon spectrum shows excellent agreement with the analytic mean field results of Ivić and Tsironis ((2006) Physica D 216 200), except for the wave vector at the midpoint of the Brillouin zone. We then relax the mean field approximation and calculate the eigenvalue spectrum of the full Hamiltonian. We show the existence of multi-phonon bound states and analyze the properties of these…

具有最近邻和次最近邻长程相互作用的量子多体系统的研究

A Study of Quantum Many-Body Systems With Nearest And Next-to-Nearest Neighbour Long-Range Interactions

研究了与短程Dyson模型有关的多体系统的散射态和束缚态。首先，我们证明了散射态可以实现为相干态，并且散射哈密顿量可以与自由系统相联系。与紧密相关的Calogero-Moser模型不同，只有一部分分波在散射后获得与能量无关的相移。相同的原因被追溯到简并的减少。本文还研究了该问题的束缚态哈密顿量，并阐明了束缚态哈密顿量的希尔伯特空间与解耦振子的希尔伯特空间之间的关系。最后，我们分析了圆上的相关模型，并通过对称性论证构造了部分激发谱。

具有近邻相互作用的量子系统的解析可解哈密顿量

Analytically solvable Hamiltonians for quantum systems with a nearest neighbour interaction

我们考虑由n个谐振子组成的线性链通过形式为$-q_r q_{r+1}$（$q_r$指的是第$r$振子的位置）的最近邻相互作用耦合而成的量子系统。原则上，这样的系统总是数值可解的，并涉及相互作用矩阵的特征值。在本文中，我们研究这样的系统是解析可解的，即当相互作用矩阵的特征值和特征向量有解析封闭表达式。这是当相互作用矩阵与离散正交多项式系统的雅可比矩阵重合时的情况。我们的研究可能的系统导致三个新的解析可解的哈密顿量：与Krawtchouk相互作用，哈恩相互作用或q-Krawtchouk相互作用。对于每一种情况，我们给出了哈密顿量的谱（解析形式），并讨论了谱的一些典型性质。

General corner states in 2D SSH model with intracelluar next-nearest-neighbour hopping

We investigate corner states in a photonic two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model on a square lattice with zero gauge flux. By considering intracelluar next-nearest-neighbor (NNN) hoppings, we discover a broad class of corner states in the 2D SSH model, and show that they are robust against certain fabrication disorders. Moreover, these corner states are located around the corners, but not at the corner points, so we refer to them as general corner states. We analytically identify that the general corner states are induced by the intracelluar NNN hoppings (long-range interaction…