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Author(s): L. Steffen [sup.1] , Y. Salathe [sup.1] , M. Oppliger [sup.1] , P. Kurpiers [sup.1] , M. Baur [sup.1] [sup.2] , C. Lang [sup.1] , C. Eichler [sup.1] , [...], Superconducting circuits combined with real-time feed-forward electronics are used to teleport a quantum state between two macroscopic solid-state systems. Efficient teleportation on demand Quantum teleportation is one of the most important elementary protocols in quantum information processing. Previous studies have achieved quantum teleportation, but usually randomly and at low rates. Two groups reporting in this issue of Nature have used contrasting methods to achieve the same aim --more efficient quantum teleportation. Takeda et al. describe the experimental realization of fully deterministic, unconditional quantum teleportation of photonic qubits -- an optimum choice for information carrying -- with overall transfer fidelities exceeding the classical limit of teleportation. The technique may facilitate the development of large-scale optical quantum networks. Steffen et al. report quantum teleportation in a solid-state system, achieving deterministic quantum teleportation in a chip-based superconducting circuit architecture. They teleport quantum states between two macroscopic systems separated by 6 mm at a rate of 10,000 per second, exceeding other reported implementations. Transmission loss in superconducting waveguides is low, so this system should be scalable to significantly larger distances, a step towards quantum communication at microwave frequencies. Engineered macroscopic quantum systems based on superconducting electronic circuits are attractive for experimentally exploring diverse questions in quantum information science.sup.1,2,3. At the current state of the art, quantum bits (qubits) are fabricated, initialized, controlled, read out and coupled to each other in simple circuits. This enables the realization of basic logic gates.sup.4, the creation of complex entangled states.sup.5,6 and the demonstration of algorithms.sup.7 or error correction.sup.8. Using different variants of low-noise parametric amplifiers.sup.9, dispersive quantum non-demolition single-shot readout of single-qubit states with high fidelity has enabled continuous.sup.10 and discrete.sup.11 feedback control of single qubits. Here we realize full deterministic quantum teleportation with feed-forward in a chip-based superconducting circuit architecture.sup.12,13,14. We use a set of two parametric amplifiers for both joint two-qubit and individual qubit single-shot readout, combined with flexible real-time digital electronics. Our device uses a crossed quantum bus technology that allows us to create complex networks with arbitrary connecting topology in a planar architecture. The deterministic teleportation process succeeds with order unit probability for any input state, as we prepare maximally entangled two-qubit states as a resource and distinguish all Bell states in a single two-qubit measurement with high efficiency and high fidelity. We teleport quantum states between two macroscopic systems separated by 6 mm at a rate of 10.sup.4 s.sup.-1, exceeding other reported implementations. The low transmission loss of superconducting waveguides is likely to enable the range of this and other schemes to be extended to significantly larger distances, enabling tests of non-locality and the realization of elements for quantum communication at microwave frequencies. The demonstrated feed-forward may also find application in error correction schemes.

The sliding-mode (SMt observer dynamics are analyzed in the frequency domain. It is shown that the SM observer is essentially a relay feedback-feedforward system. It is feedback with respect to the measured variable of the system being observed, and the feedforward with respect to the control applied to the system being observed. Having noted this, the input-output properties of observer dynamics are analyzed with the use of the locus of a perturbed relay system (LPRS) method. The performance of the observer is assessed via the use of the frequency response techniques. An example of performance analysis of the observer dynamics in the frequency domain is given. Index Terms--Frequency domain, nonlinear observers, sliding modes (SMs).