We present a general, systematic, and efficient method for decomposing any given exponential operator of bosonic mode operators, describing an arbitrary multimode Hamiltonian evolution, into a set of universal unitary gates. Although our approach is mainly oriented towards continuous-variable quantum computation, it may be used more generally whenever quantum states are to be transformed deterministically, e.g., in quantum control, discrete-variable quantum computation, or Hamiltonian simulation. We illustrate our scheme by presenting decompositions for various nonlinear Hamiltonians including quartic Kerr interactions. Finally, we conclude with two potential experiments utilizing offline-prepared optical cubic states and homodyne detections, in which quantum information is processed optically or in an atomic memory using quadratic light-atom interactions.
We present a method for implementing a weak optical Kerr interaction (single-mode Kerr Hamiltonian) in a measurement-based fashion using the common set of universal elementary interactions for continuous-variable quantum computation. Our scheme is a conceptually distinct alternative to the use of naturally occurring, weak Kerr nonlinearities or specially designed nonlinear media. Instead, we propose to exploit suitable off-line prepared quartic ancilla states together with beam splitters, squeezers, and homodyne detectors. For perfect ancilla states and ideal operations, our decompositions for obtaining the measurement-based Kerr Hamiltonian lead to a realization with near-unit fidelity. Nonetheless, even by using only approximate ancilla states in the form of superposition states of up to four photons, high fidelities are still attainable. Our scheme requires four elementary operations and its deterministic implementation corresponds to about 10 ancilla-based gate teleportations. We test our measurement-based Kerr interaction against an ideal Kerr Hamiltonian by applying them both to weak coherent states and single-photon superposition states
We present a general technique for deterministically implementing a multi-mode nonlinear coupling between several propagating microwave or optical modes in quantum circuits. The measurement induced technique combines specifically prepared resource states together with feasible feed-forward operations. We explore several ways of generating the suitable resource states and discuss their difference on an illustrative example of cubic coupling between two modes. We also show that the required entangled states with requisite nonlinear properties can be already generated in the present day experiments.
We study propagation of short laser pulses in a Bose-Einstein condensate taking into account dispersive effects under the conditions for electromagnetically induced transparency. We calculate dispersion coefficients using typical experimental parameters of slow-light schemes in condensates. By numerically propagating the laser pulse, and referring to theoretical estimations, we determine the conditions for which dispersion starts to introduce distortions on the pulse shape.
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