Multimode entanglement is an essential resource for quantum information processing and quantum metrology. However, multimode entangled states are generally constructed by targeting a specific graph configuration. This yields to a fixed experimental setup that therefore exhibits reduced versatility and scalability. Here we demonstrate an optical on-demand, reconfigurable multimode entangled state, using an intrinsically multimode quantum resource and a homodyne detection apparatus. Without altering either the initial squeezing source or experimental architecture, we realize the construction of thirteen cluster states of various sizes and connectivities as well as the implementation of a secret sharing protocol. In particular, this system enables the interrogation of quantum correlations and fluctuations for any multimode Gaussian state. This initiates an avenue for implementing on-demand quantum information processing by only adapting the measurement process and not the experimental layout.

Starting from a quantum two-mode Bose-Hubbard Hamiltonian we determine the ground state properties, momentum distribution and dynamical evolution for a Bose Josephson junction realized by an ultracold Bose gas in a double-well trap. Varying the well asymmetry we identify Mott-like regions of parameters where number fluctuations are suppressed and the interference fringes in the momentum distribution are strongly reduced. We also show how Schroedinger cat states, realized from an initially phase coherent state by a sudden rise of the barrier among the two wells, will give rise to a destructive interference in the time-dependent momentum distribution.PACS numbers: 03.75.Mn Superconductor Josephson junctions are a paradigmatic example of macroscopic quantum coherence. The underlying physical mechanism is the Josephson effect [1]: two superconductors connected by a weak link have coherent dynamical behavior determined by the relative macroscopic phase of the superconducting condensates. Josephson junctions have been used to discuss fundamental concepts in quantum mechanics [2], perform precision measurements [3], and are now promising candidates to implement quantum information devices [4]. One important feature of superconducting Josephson junctions is the possibility to precisely control and adjust the state of the system by varying external parameters, eg a gate-voltage or magnetic flux.Bose Josephson junctions have been only recently proposed [5], and realized experimentally [6], and many issues remain open. In the simplest configuration a Bose Josephson junction is realized by confining an ultracold Bose gas in a double-well potential. This configuration can be described using a two-mode model in which the bosons occupy the lowest level in each well. In the "classical" regime of large particle numbers and weak repulsive interactions the gas is well described by the Gross-Pitaevskii equation which, within the two-mode approximation, can be recast in the form of generalized Josephson equations for the time evolution of the relative phase and population imbalance among the two wells [5]. These equations differ from the original ones used for superconductor Josephson junctions [3] by the presence of a nonlinear coupling among the phase and populationimbalance variables. This term originates from bosonboson interactions in the mean-field approximation and gives rise to a rich dynamical behavior, displaying self trapping and π oscillations [5].In this Letter we focus on the mesoscopic "quantum" regime beyond the Gross-Pitaevskii equation, in the limit of strong interactions and/or smaller values of N . This gets within reach of current experiments [7]. As interactions are increased phase fluctuations become more and more important while number fluctuations are suppressed; the ground state of the system approaches a regime which can be viewed as a mesoscopic Mott insulator. During the time evolution the phase coherence first degrades ("phase diffusion" [8]), but, in a closed quantum system, periodically revives, as ...

Present-day, noisy, small or intermediate-scale quantum processors-although far from fault tolerant-support the execution of heuristic quantum algorithms, which might enable a quantum advantage, for example, when applied to combinatorial optimization problems. On small-scale quantum processors, validations of such algorithms serve as important technology demonstrators. We implement the quantum approximate optimization algorithm on our hardware platform, consisting of two superconducting transmon qubits and one parametrically modulated coupler. We solve small instances of the NP (nondeterministic polynomial time)-complete exact-cover problem, with 96.6% success probability, by iterating the algorithm up to level two.