Quantum computers promise ultrafast performance of certain tasks 1 . Experimentally appealing, measurement-based quantum computation (MBQC) 2 requires an entangled resource called a cluster state 3 , with long computations requiring large cluster states. Previously, the largest cluster state consisted of 8 photonic qubits 4 or light modes 5 , while the largest multipartite entangled state of any sort involved 14 trapped ions 6 . 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 multiplexing light modes in the time domain. We deterministically generate and fully characterise a continuous-variable cluster state 7,8 containing more than 10,000 entangled modes. This is, by 3 orders of magnitude, the largest entangled state ever created to date. The entangled modes are individually addressable wavepackets of light in two beams. Furthermore, we present an efficient scheme for MBQC on this cluster state based on sequential applications of quantum teleportation.Originally formulated as a demonstration as to why quantum mechanics must be incomplete in the famous 1935 Einstein-Podolsky-Rosen (EPR) paradox 9 , entanglement is now recognized as a signature feature of quantum physics 10 , and it plays a central role in various quantum information processing (QIP) protocols 1,11 . For example, the bipartite entangled state known as an EPR state 9 is a resource for quantum teleportation (QT), whereby a quantum state is transferred from one location to another without physical transfer of the quantum information 12-14 .Measurement-based quantum computation (MBQC) 2,7,8,[15][16][17][18] , which is based on the QT of information and logic gates, requires the special class of multipartite entangled resource states known as cluster states 3 . The number of entangled quantum entities and their entanglement structure (represented by a graph) determines the resource space available for computation.Ultra-large-scale QIP (which could be based on MBQC) will require ultra-large-scale entangled 2 states 2,7,8 .In the vast majority of optical experiments, quantum modes are distinguished from each other by their spatial location. This leads to an inherent lack of scalability as each additional entangled party requires an increase in laboratory equipment and dramatically increases the complexity of the optical network 19,20 . Further, due to the probabilistic nature of photon pair generation, demonstrations involving the postselection of photonic qubits 4,15,16 suffer from dramatically reduced event success rates with each additional qubit.One method to overcome this problem of scalability is to deterministically encode the modes within one beam. Entanglement between quadrature-phase amplitudes in continuouswave laser beams has been deterministically created and exploited in QIP 5,13,14,[17][18][19][21][22][23] , even though the quantum correlations are finite. Previous attempts to deterministically create cluster ...

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 consider measurement-based quantum computation that uses scalable continuous-variable cluster states with a one-dimensional topology. The physical resource, known here as the dual-rail quantum wire, can be generated using temporally multiplexed offline squeezing and linear optics or by using a single optical parametric oscillator. We focus on an important class of quantum gates, specifically Gaussian unitaries that act on single modes, which gives universal quantum computation when supplemented with multi-mode operations and photon-counting measurements. The dual-rail wire supports two routes for applying single-qumode Gaussian unitaries: the first is to use traditional one-dimensional quantum-wire cluster-state measurement protocols. The second takes advantage of the dual-rail quantum wire in order to apply unitaries by measuring pairs of qumodes called macronodes. We analyze and compare these methods in terms of the suitability for implementing single-qumode Gaussian measurement-based quantum computation.

One-way quantum computation is a very promising candidate to fulfill the capabilities of quantum information processing. Here we demonstrate an important set of unitary operations for continuous variables using a linear cluster state of four entangled optical modes. These operations are performed in a fully measurement-controlled and completely unconditional fashion. We implement three different levels of squeezing operations and a Fourier transformation, all of which are accessible by selecting the correct quadrature measurement angles of the homodyne detections. Though not sufficient, these linear transformations are necessary for universal quantum computation.