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 ...

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.

Quantum spin liquid is an enigmatic entity that is often hard to characterize within the conventional framework of condensed matter physics. We here present theoretical and numerical evidence for the characterization of a quantum spin liquid phase extending from the exact ground state to a finite critical temperature. We investigate a three-dimensional variant of the Kitaev model on a hyperhoneycomb lattice in the limit of strong anisotropy; the model is mapped onto an effective Ising-type model, where elementary excitations consist of closed loops of flipped Ising-type variables on a diamond lattice. Analyzing this effective model by Monte Carlo simulation, we find a phase transition from quantum spin liquid to paramagnet at a finite critical temperature Tc accompanied with divergent singularity of the specific heat. We also compute the magnetic properties in terms of the original quantum spins. We find that the magnetic susceptibility exhibits a broad hump above Tc, while it obeys the Curie law at high temperature and approaches a nonzero Van Vleck-type constant at low temperature. Although the susceptibility changes continuously at Tc, its temperature derivative shows critical divergence at Tc. We also clarify that the dynamical spin correlation function is momentum independent but shows quantized peaks corresponding to the discretized excitations. Although the phase transition accompanies no apparent symmetry breaking in terms of the Ising-type variables as well as the original quantum spins, we characterize it from a topological viewpoint. We find that, by defining the flux density for loops of the Isingtype variables, the transition is interpreted as the one occurring from the zero-flux quantum spin liquid to the nonzero-flux paramagnet; the latter has a Coulombic nature due to the local constraints. The role of global constraints on the Ising-type variables is examined in comparison with the results in the two-dimensional loop model. A correspondence of our model to the Ising model on a diamond lattice is also discussed. A possible relevance of our results to the recently-discovered hyperhoneycomb compound, β-Li2IrO3, is mentioned.

We demonstrate an optical quantum nondemolition (QND) interaction gate with a bandwidth of about 100 MHz. Employing this gate, we are able to perform QND measurements in real time on randomly fluctuating signals. Our QND gate relies upon linear optics and offline-prepared squeezed states. In contrast to previous demonstrations on narrow sideband modes, our gate is compatible with non-Gaussian quantum states temporally localized in a wave-packet mode, and thus opens the way for universal gate operations and realization of quantum error correction.

No abstract