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 ...

Entanglement is the key resource for measurement-based quantum computing. It is stored in quantum states known as cluster states, which are prepared offline and enable quantum computing by means of purely local measurements. Universal quantum computing requires cluster states that are both large and possess (at least) a two-dimensional topology. Continuous-variable cluster states—based on bosonic modes rather than qubits—have previously been generated on a scale exceeding one million modes, but only in one dimension. Here, we report generation of a large-scale two-dimensional continuous-variable cluster state. Its structure consists of a 5- by 1240-site square lattice that was tailored to our highly scalable time-multiplexed experimental platform. It is compatible with Bosonic error-correcting codes that, with higher squeezing, enable fault-tolerant quantum computation.

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 inseparable light modes to around ten thousands, by continuous feedback control of the optical system.

We present a concept of non-Gaussian measurement composed of a non-Gaussian ancillary state, linear optics and adaptive heterodyne measurement, and on the basis of this we also propose a simple scheme of implementing a quantum cubic gate on a traveling light beam. In analysis of the cubic gate in the Heisenberg representation, we find that nonlinearity of the gate is independent from nonclassicality; the nonlinearity is generated solely by a classical nonlinear adaptive control in a measurement-and-feedforward process while the nonclassicality is attached by the non-Gaussian ancilla that suppresses excess noise in the output. By exploiting the noise term as a figure of merit, we consider the optimum non-Gaussian ancilla that can be prepared within reach of current technologies and discuss performance of the gate. It is a crucial step towards experimental implementation of the quantum cubic gate.

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.