QUROPE Quantum Information Processing and Communication in Europe

On August 6 HP Labs' researcher Vinay Deolalikar sent the following letter to his fellows researchers in HP Labs:

"Dear Fellow Researchers,
I am pleased to announce a proof that P is not equal to NP, which is attached in 10pt and 12pt fonts

The proof required the piecing together of principles from multiple areas within mathematics. The major effort in constructing this proof was uncovering a chain of conceptual links between various fields and viewing them through a common lens. Second to this were the technical hurdles faced at each stage in the proof.

This work builds upon fundamental contributions many esteemed researchers have made to their fields. In the presentation of this paper, it was my intention to provide the reader with an understanding of the global framework for this proof. Technical and computational details within chapters were minimized as much as possible.

We analyze in detail the so-called pushing gate for trapped ions, introducing a time-dependent harmonic approximation for the external motion. We show how to extract the average fidelity for the gate from the resulting semiclassical simulations. We characterize and quantify precisely all types of errors coming from the quantum dynamics and reveal that slight nonlinearities in the ion-pushing force can have a dramatic effect on the adiabaticity of gate operation.

The uncertainty principle bounds the uncertainties about the outcomes of two incompatible measurements on a particle. However, if the particle is prepared entangled with a quantum memory it is possible to predict the outcomes for both measurement choices precisely. In this work, the authors extend the uncertainty principle to this scenario, providing a lower bound on the uncertainties which depends on the amount of entanglement between the particle and the quantum memory.

Perfect states are those quantum states from which a perfectly secure cryptographic key can be extracted. They present the basic unit of quantum privacy. In this work we show that all states belonging to this class violate a Bell inequality. This result establishes a connection between perfect privacy and non-locality in the quantum domain.

A rigorous quantum theory of atomic collisions in the presence of radio frequency (rf) magnetic fields is developed and applied to elucidate the effects of combined dc and rf magnetic fields on ultracold collisions of Rb atoms. We show that rf fields can be used to induce Feshbach resonances, which can be tuned by varying the amplitude and frequency of the rf field.

We introduce a scheme for efficiently describing pure states of strongly correlated fermions in higher dimensions using unitary circuits featuring a causal cone. A local way of computing local expectation values is presented. We formulate a dynamical reordering scheme, corresponding to time-adaptive Jordan-Wigner transformation, that avoids nonlocal string operators. Primitives of such a reordering scheme are highlighted. Fermionic unitary circuits can be contracted with the same complexity as in the spin case.

Complex networks represent one of the most active research topics, as they found application in many different scenarios, from studied of internet to propagation of diseases. In this work, the authors extend the concept of a random network, arguably the simplest example of complex network, to the quantum domain. They show that the obtained model has a completely distinct behavior of the critical probabilities at which different subgraphs appear.

Matrix product states (MPS) represent a powerful ansatz for the computation of ground state properties of local Hamiltonians. In this work, the authors define MPS in the continuum limit, without any reference to an underlying lattice parameter. This allows extending the density matrix renormalization group and variational matrix product state formalism to quantum field theories and continuum models in 1 spatial dimension.

• quantum information theory
• quantum optical implementations of quantum information ideas
• quantum many-body theory

The aim of the workshop is to explore how experiments with ultracold gases can address key open problems in many-body quantum physics. Among other things it will focus on the following topics: fundamental limitations and new ideas in quantum simulation of unsolved models such as the Hubbard model; novel cooling schemes based on ideas from quantum information as well as atomic and many-body physics; emergent phenomena in non-equilibrium quantum dynamics; novel quantum magnetism in Bose and Fermi systems; realizing and probing topologically ordered states.