Continuous-variable Gaussian cluster states are a potential resource for universal quantum computation. They can be efficiently and unconditionally built from sources of squeezed light using beam splitters. Here we report on the generation of three different kinds of continuous-variable four-mode cluster states. In our realization, the resulting cluster-type correlations are such that no corrections other than simple phase-space displacements would be needed when quantum information propagates through these states. At the same time, the inevitable imperfections from the finitely squeezed resource states and from additional thermal noise are minimized, as no antisqueezing components are left in the cluster states.
We introduce an efficient scheme to correct errors due to the finite squeezing effects in continuous-variable cluster states. Specifically, we consider the typical situation where the class of algorithms consists of input states that are known. By using the knowledge of the input states, we can diagnose exactly what errors have occurred and correct them in the context of temporal continuous-variable cluster states. We illustrate the error correction scheme for single-mode and two-mode unitaries implemented by spatial continuous-variable cluster states. We show that there is no resource advanta…
The immense scalability of continuous-variable cluster states motivates their study as a platform for quantum computing, with fault tolerance possible given sufficient squeezing and appropriately encoded qubits [Menicucci, PRL 112, 120504 (2014)]. Here, we expand the scope of that result by showing that additional anti-squeezing has no effect on the fault-tolerance threshold, removing the purity requirement for experimental continuous-variable cluster-state quantum computing. We emphasize that the appropriate experimental target for fault-tolerant applications is to directly measure 15-17 dB o…
Quantum secret sharing with continuous-variable cluster states
我们扩展了簇态量子秘密共享的形式主义，如Markham和Sanders [Phys.Rev.A78，042309（2008）]和Keet等人[Phy. Rev. A 82，062315（2010）]，到连续变量方案。我们表明，经典和量子信息可以通过分配连续变量集群状态通过公共或私人渠道共享。我们发现，如果集团态是无限压缩的，对手的结构是完全否认从秘密，但如果采用一个现实的双压缩状态将泄露一些秘密信息。我们建议的基准来评估的安全性，在挤压的情况下。对于经典秘密的共享，我们借用了连续变量量子密钥分发的技术来计算秘密共享率。对于量子态的共享，我们估计了从每个团簇态中提取的用于隐形传态的纠缠量。
Cluster states are an essential component in one-way quantum computation protocols. We present two schemes to generate addressable continuous-variable cluster states from quadrature squeezed cylindrically polarized modes. By including polarization in addition to the transverse spatial degree of freedom, elementary cluster states can be created in which four cluster nodes co-propagate within one paraxial vector beam. This approach is fundamentally compatible with existing time-multiplexed schemes that have been used to create the largest cluster states to date. We implement a proof-of-principle…
Large-scale continuous variable (CV) cluster state is necessary in quantum information processing based on measurement-based quantum computing (MBQC). Specially, generating large-scale CV cluster state multiplexed in time domain is easier to implement and has strong scalability in experiment. Here one-dimensional (1D) large-scale dual-rail CV cluster states multiplexed both in time and frequency domains are parallelly generated, which can be further extended to three-dimensional (3D) CV cluster state by combining two time-delay NOPA systems with beamsplitters. It is shown that the number of pa…
We present an algorithm to reliably generate various quantum states critical to quantum error correction and universal continuous-variable (CV) quantum computing, such as Schrödinger cat states and Gottesman-Kitaev-Preskill (GKP) grid states, out of Gaussian CV cluster states. Our algorithm is based on the Photon-counting-Assisted Node-Teleportation Method (PhANTM), which uses standard Gaussian information processing on the cluster state with the only addition of local photon-number-resolving measurements. We show that PhANTM can apply polynomial gates and embed cat states within the cluster. …
We show that measurement-based quantum computation on scalable continuous-variable (CV) cluster states admits more quantum-circuit flexibility and compactness than similar protocols for standard square-lattice CV cluster states. This advantage is a direct result of the macronode structure of these states---that is, a lattice structure in which each graph node actually consists of several physical modes. These extra modes provide additional measurement degrees of freedom at each graph location, which can be used to manipulate the flow and processing of quantum information more robustly and with…
Bipartite Entanglement in Continuous-Variable Cluster States
我们研究了高斯团簇态的纠缠特性，它被认为是连续变量量子计算的通用资源。一个中心目标是比较理想化的集群状态定义使用正交本征态，具有无限压缩，不能存在于自然界中，与高斯近似，这是实验上可以访问。采用广泛使用的定义，我们首先审查的关键概念，通过分析的过程中的隐形传态沿着一个连续变量的量子线的语言的矩阵产品状态。接下来，我们考虑线的二分纠缠特性，提供分析结果。我们继续到网格簇状态，这对于量子比特的情况是通用的。为了扩展我们对两体纠缠的分析，我们采用了熵纠缠宽度，这是Van den Nest M等人最近提出的一种专门的纠缠度量，物理修订信函97 150504（2006），使其定义适应连续变量的背景。最后，我们加入了光子损失的影响，扩展我们的论点混合状态。累积我们的研究结果点的理想化和高斯集群状态的属性的关键差异。即使是适度的损失率被发现强烈限制纠缠的量。我们讨论了基于测量的量子计算的连续变量类似物的潜力的影响。
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 …
Entangling the optical frequency comb: simultaneous generation of multiple 2x2 and 2x3 continuous-variable cluster states in a single optical parametric oscillator
In recent quantum optical continuous-variable experiments, the number of fully inseparable light modes has drastically increased by introducing a multiplexing scheme either in the time domain or in the frequency domain. Here, modifying the time-domain multiplexing experiment reported in Nature Photonics 7, 982 (2013), we demonstrate successive generation of fully inseparable light modes for more than one million modes. The resulting multi-mode state is useful as a dual-rail CV cluster state. We circumvent the previous problem of optical phase drifts, which has limited the number of fully insep…
One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but non-universal, continuous-variable cluster states were recently demonstrated separately in the time and frequency domains. We propose to combine these approaches into a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle up to ($3\times 10^3$ frequencies) $\times$ (unlimited number of temporal modes) into a new and computationally universal continuous-variable cluster state. We in…
Quantum computers promise ultrafast performance of certain tasks. Experimentally appealing, measurement-based quantum computation (MBQC) requires an entangled resource called a cluster state, with long computations requiring large cluster states. Previously, the largest cluster state consisted of 8 photonic qubits or light modes, while the largest multipartite entangled state of any sort involved 14 trapped ions. These implementations involve quantum entities separated in space, and in general, each experimental apparatus is used only once. Here, we circumvent this inherent inefficiency by mul…
Due to its unique scalability potential, continuous variable quantum optics is a promising platform for large scale quantum computing. In particular, very large cluster states with a two-dimensional topology that are suitable for universal quantum computing and quantum simulation can be readily generated in a deterministic manner, and routes towards fault-tolerance via bosonic quantum error-correction are known. In this article we propose a complete measurement-based quantum computing architecture for the implementation of a universal set of gates on the recently generated two-dimensional clus…
Continuous-variable (CV) cluster states are a universal quantum computing platform that has experimentally out-scaled qubit platforms by orders of magnitude. Room-temperature implementation of CV cluster states has been achieved with quantum optics by using multimode squeezed Gaussian states. It has also been proven that fault tolerance thresholds for CV quantum computing can be reached at realistic squeezing levels. In this paper, we show that standard approaches to design and characterize CV cluster states can miss entanglement present in the system. Such hidden entanglement may be used to i…
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…
Five-wave-packet quantum error correction based on continuous-variable cluster entanglement
量子纠错在量子通信和量子计算中保护量子态不受噪声和退相干的影响，使人们能够进行故障洪流量子信息处理。实验证明了一种针对单一随机错误的五波包码量子纠错方案，其理论模型是由S. L. Braunstein和T. A.沃克利用连续变量团簇纠缠态的五个子模作为五个编码通道。特别地，在我们的编码方案中，输入态的信息只分布在五个通道中的三个通道上，因此在剩下的两个通道中出现的任何错误都不会影响输出态，即输出量子态不受这两个通道中的错误的影响。对真空态和压缩态的单通道随机误差进行了修正，得到的输出态的量子效率超过了相应的经典极限。
Continuous-variable (CV) cluster states are a universal resource for fault-tolerant quantum computation when supplemented with the Gottesman-Kitaev-Preskill (GKP) bosonic code. We generalize the recently introduced subsystem decomposition of a bosonic code [Phys. Rev. Lett. 125, 040501 (2020)], and we use it to analyze CV cluster-state quantum computing with GKP states. Specifically, we decompose squeezed vacuum states and approximate GKP states to reveal their encoded logical information, and we decompose several gates crucial to CV cluster-state quantum computing. Then, we use the subsystem …
Cluster state plays a crucial role in the one-way quantum computation. Here, we propose and experimentally demonstrate a new scheme to prepare an ultrahigh-fidelity four-photon linear cluster state via spontaneous parametric down-conversion process. The state fidelity is measured to be $0.9517\pm0.0027$. Our scheme can be directly extended to more photons to generate N-qubit linear cluster state. Furthermore, our scheme is optimal for generating photonic linear cluster states in the sense of achieving the maximal success probability and having the simplest strategy. The key idea is that the ph…
We study the quantum controlled and probabilistic teleportation protocol via a four-cluster state (Front. Phys. (2017) 12: 120306). The protocol cannot achieve the goal that if the teleportation fails, it can be repeated without copies of the teleported state. And the reason is that all the information of the teleported state shifts to the receiver's particle after Bell measurement and the information cannot shift back to the sender without other entangled states. To realize the claimed goal, a new quantum controlled and probabilistic teleportation protocol using the same four-cluster state is…
