Jens Siewert

Detection of geometric phases in superconducting nanocircuits

When a quantum-mechanical system undergoes an adiabatic cyclic evolution, it acquires a geometrical phase factor in addition to the dynamical one; this effect has been demonstrated in a variety of microscopic systems. Advances in nanotechnology should enable the laws of quantum dynamics to be tested at the macroscopic level, by providing controllable artificial two-level systems (for example, in quantum dots and superconducting devices). Here we propose an experimental method to detect geometric phases in a superconducting device. The setup is a Josephson junction nanocircuit consisting of a superconducting electron box. We discuss how interferometry based on geometrical phases may be realized, and show how the effect may be applied to the design of gates for quantum computation.

Non-abelian holonomies, charge pumping, and quantum computation with Josephson junctions

Non-Abelian holonomies can be generated and detected in certain superconducting nanocircuits. Here we consider an example where the non-Abelian operations are related to the adiabatic charge dynamics of the Josephson network. We demonstrate that such a device can be applied both for adiabatic charge pumping and as an implementation of a quantum computer.

Natural two-qubit gate for quantum computation using the XY interaction

The two-qubit interaction Hamiltonian of a given physical implementation determines whether or not a two-qubit gate such as the controlled-NOT (cNOT) gate can be realized easily. It can be shown that, e.g., with the XY interaction more than one two-qubit operation is required in order to realize the CNOT operation. Here we propose a two-qubit gate for the X Y interaction which combines the CNOT and SWAP operations. By using this gate quantum circuits can be implemented efficiently, even if only nearest-neighbor coupling between the qubits is available.

Fidelity and Leakage of Josephson Qubits

The unit of quantum information is the qubit, a vector in a two-dimensional Hilbert space. On the other hand, quantum hardware often operates in two-dimensional subspaces of vector spaces of higher dimensionality. The presence of higher quantum states may affect the accuracy of quantum information processing. In this Letter we show how to cope with {\em quantum leakage} in devices based on small Josephson junctions. While the presence of higher charge states of the junction reduces the fidelity during gate operations we demonstrate that errors can be minimized by appropriately designing and operating the gates.

Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states.

The first characterization of mixed-state entanglement was achieved for two-qubit states in Werners seminal work [Phys. Rev. A 40, 4277 (1989)]. A physically important extension concerns mixtures of a pure entangled state [such as the Greenberger-Horne-Zeilinger (GHZ) state] and the unpolarized state. These mixed states serve as benchmark for the robustness of multipartite entanglement. They share the symmetries of the GHZ state. We call such states GHZ symmetric. Here we give a complete description of the entanglement in the family of three-qubit GHZ-symmetric states and, in particular, of the three-qubit generalized Werner states. Our method relies on the appropriate parametrization of the states and on the invariance of entanglement properties under general local operations. An application is the definition of a symmetrization witness for the entanglement class of arbitrary three-qubit states.

ENTANGLEMENT MONOTONES AND MAXIMALLY ENTANGLED STATES IN MULTIPARTITE QUBIT SYSTEMS

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call comb in reference to the hairy-ball theorem. For qubits (i.e. spin 1/2) the combs are automatically invariant under SL (2, ℂ). This implies that the filters obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-, five- and six-qubit entanglement.

Negativity as an estimator of entanglement dimension.

Among all entanglement measures negativity arguably is the best known and most popular tool to quantify bipartite quantum correlations. It is easily computed for arbitrary states of a composite system and can therefore be applied to discuss entanglement in an ample variety of situations. However, as opposed to logarithmic negativity, its direct physical meaning has not been pointed out yet. We show that the negativity can be viewed as an estimator of how many degrees of freedom of two subsystems are entangled. As it is possible to give lower bounds for the negativity even in a device-independent setting, it is the appropriate quantity to certify quantumness of both parties in a bipartite system and to determine the minimum number of dimensions that contribute to the quantum correlations.

Lava channel formation during the 2001 eruption on Mount Etna: evidence for mechanical erosion.

We report the direct observation of a peculiar lava channel that was formed near the base of a parasitic cone during the 2001 eruption on Mount Etna. Erosive processes by flowing lava are commonly attributed to thermal erosion. However, field evidence strongly suggests that models of thermal erosion cannot explain the formation of this channel. Here, we put forward the idea that the essential erosion mechanism was abrasive wear. By applying a simple model from tribology we demonstrate that the available data agree favorably with our hypothesis. Consequently, we propose that erosional processes resembling the wear phenomena in glacial erosion are possible in a volcanic environment.

Mechanical erosion by flowing lava

Hot lava is a viscous fluid that, driven by gravity, moves along the Earths surface. Intuitively, one attributes constructional properties to lava–it accumulates in volcanic landforms, compound lava fields and, in the end, entire mountains. On the other hand, there are also examples of the erosive power of lava: on Earth and especially on other planets in the Solar System, there exist channels incised by flowing lava. The origins of these erosive features have long been debated among volcanologists and planetologists. The dominant paradigm is thermal erosion, although it leaves many questions open. After the 2001 eruption on Mount Etna we found a lava channel whose features cannot be explained in the frame of thermal erosion. On the basis of our observations, we have developed a model for mechanical erosion that explains the main field observations, and opens alternative ways to describe erosion by flowing lava.

Quantum Algorithms for Josephson Networks

We analyze possible implementations of quantum algorithms in a system of (macroscopic) Josephson charge qubits. System layout and parameters to realize the Deutsch algorithm with up to three qubits are provided. Special attention is paid to the necessity of entangled states in the various implementations. Further, we demonstrate explicitly that the gates to implement the Bernstein-Vazirani algorithm can be realized by using a system of uncoupled qubits.