The concept of qudit (a d-level system) cluster state is proposed by generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001)) according to the finite dimensional representations of quantum plane algebra. We demonstrate their quantum correlations and prove a theorem which guarantees the availability of the qudit cluster states in quantum computation. We explicitly construct the network to show the universality of the one-way computer based on the defined qudit cluster states and single-qudit measurement. And the corresponding protocol of implementing one-way quantum computer can be suggested with the high dimensional "Ising" model which can be found in many magnetic systems.
In this paper, we study the transformations that are obtained in one-way quantum computation on continuous-variable cluster states of various configurations. Of all possible cluster configurations, we choose those that are suitable for universal Gaussian operations.
In this paper, we estimate the errors of Gaussian transformations implemented using one-way quantum computations on cluster states of various configurations. From all possible cluster state configurations, we choose those that give the smallest computation error. Furthermore, we evaluate errors in hybrid computational schemes, in which Gaussian operations are performed using one-way computations with additional linear transformations. As a result, we find the optimal strategy for the implementation of universal Gaussian computations with minimal errors.
In this study, we demonstrate the possibility of the implementation of universal Gaussian computation on a two-node cluster state ensemble. We consider the phase-locked sub-Poissonian lasers, which radiate the bright light with squeezed quadrature, as the resource to generate these states.
Cluster state quantum computation for many-level systems
量子计算的簇态模型[Phys. Rev. Lett. 86，5188]概述了一个方案，允许人们使用测量一个大的纠缠量子系统在什么是所谓的集群状态进行量子计算。该模型本身和许多致力于它的工作涉及使用纠缠量子比特。在本文中，我们考虑的问题，而不是使用纠缠量子点。我们提出了一个完整的框架，簇态量子计算使用qudits，它不仅包含了原来的量子比特模型的功能，但也包含了新的自适应计算的想法：通过改变经典计算，有助于纠正错误的模型中固有的，可以改变实现的量子计算。这个特性是通过使用qudits时出现的额外自由度而产生的。最后，对于素数维，我们给出了一个非常明确的描述模型，利用相互无偏的基础。
Measurement-based quantum computation with continuous variables in an optical setup shows the great promise towards implementation of large-scale quantum computation, where the time-domain multiplexing approach enables us to generate the large-scale cluster state used to perform measurement-based quantum computation. To make effective use of the advantage of the time-domain multiplexing approach, in this paper, we propose the method to generate the large-scale 3-dimensional cluster state which is a platform for topologically protected measurement-based quantum computation. Our method combines …
A Flexible GKP-State-Embedded Fault-Tolerant Quantum Computation Configuration Based on a Three-Dimensional Cluster State
Shanxi University（山西大学）；State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（量子光学技术和器件国家重点实验室，山西大学）；College of Physics and Electronic Engineering, Shanxi University（山西大学物理电子工程学院）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
Fault-tolerant quantum computation with cluster states
由Raussendorf和Briegel引入的单向量子计算模型[Phys. Rev. Lett. 86（22），5188-5191（2001）]表明可以仅使用被称为簇态的固定纠缠资源和自适应单量子比特测量来进行量子计算。这个模型是几个实用的量子计算方案的基础，包括一个有希望的基于团簇态的光量子计算方案[M。A. Nielsen，arXiv：quant-ph/0402005，accepted to appear in Phys. Rev. Lett.].一个重要的开放问题是，这种建议是否是可扩展的存在物理现实的噪音。在本文中，我们证明了两个阈值定理，这表明，可扩展的容错量子计算可以实现基于集群状态的实现，提供的实现中的噪声是低于某个恒定的阈值。我们的第一个阈值定理适用于一类实现中，纠缠门应用确定性，但有少量的噪音。我们希望这个阈值能够适用于各种各样的物理系统。我们的第二个阈值定理是专门适应的建议，如光学集群状态的建议，其中使用非确定性纠缠门。一个关键的技术组成部分，我们的证明是两个强大的定理，关系到性能的噪音单一的操作限制作用于状态空间的子空间，这些操作的扩展作用于整个状态空间。
In this paper, we investigate the error correction of universal Gaussian transformations obtained in the process of continuous-variable quantum computations. We have tried to bring our theoretical studies closer to the actual picture in the experiment. When investigating the error correction procedure, we have considered that both the resource GKP state itself and the entanglement transformation are imperfect. In reality, the GKP state has a finite width associated with the finite degree of squeezing, and the entanglement transformation is performed with error. We have considered a hybrid sche…
In this paper, we propose two strategies for decreasing the error of arbitrary single-mode Gaussian transformations implemented using one-way quantum computation on a four-node linear cluster state. We show that it is possible to minimize the error of the arbitrary single-mode Gaussian transformation by a proper choice of the weight coefficients of the cluster state. We modify the computation scheme by adding a non-Gaussian state obtained using a cubic phase gate as one of the nodes of the cluster. This further decreases the computation error. We evaluate the efficiencies of the proposed optim…
We show that 2D fractal subsystem symmetry-protected topological phases may serve as resources for universal measurement-based quantum computation. This is demonstrated explicitly for two cluster models known to lie within fractal symmetry-protected topological phases, and computational universality is shown to persist throughout those phases. One of the models considered is simply the cluster model on the honeycomb lattice in one limit. We discuss the importance of rigid subsystem symmetries, as opposed to global or $(\text{D}-1)$-form symmetries, in this context.
Measurement-based quantum computation offers exponential computational speed-up via simple measurements on a large entangled cluster state. We propose and demonstrate a scalable scheme for the generation of photonic cluster states suitable for universal measurement-based quantum computation. We exploit temporal multiplexing of squeezed light modes, delay loops, and beam-splitter transformations to deterministically generate a cylindrical cluster state with a two-dimensional (2D) topological structure as required for universal quantum information processing. The generated state consists of more…
What kinds of symmetry-protected topologically ordered (SPTO) ground states can be used for universal measurement-based quantum computation in a similar fashion to the 2D cluster state? 2D SPTO states are classified not only by global on-site symmetries but also by subsystem symmetries, which are fine-grained symmetries dependent on the lattice geometry. Recently, all states within so-called SPTO cluster phases on the square and hexagonal lattices have been shown to be universal, based on the presence of subsystem symmetries and associated structures of quantum cellular automata. Motivated by …
