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Robust atomic quantum information processing networks in periodic lattice structures

Final Activity Report Summary - RAQUIN (Robust atomic quantum information processing networks in periodic lattice structures)

Quantum information processing has fascinating features and offers outstanding potentials. Quantum computers promise to be much more powerful for certain computational tasks than classical computers and quantum communication allows for absolute secure crypto systems. The main objective of the Marie-Curie Intra European Fellowship project 'Robust atomic quantum information processing networks in periodic lattice structures' was to invent and enhance techniques within the field of quantum information processing towards a reliable and robust technology.

In our work we theoretically considered different schemes to reach this goal. In a major part of our work we exploited the concept of decoherence free subspaces, i.e. a quantum memory which is immune to noise and can thus be used to reliably store quantum information. However, the manipulation of the fundamental carrier of quantum information, the quantum bits or qubits, which are stored in this type of memory, is a highly non trivial task. For quantum information processing it is required to initialise, measure and manipulate single qubits, via single qubit gates, and to perform logical two qubit operations, via two qubit gates.

Within this project we developed a feasible scheme where decoherence free qubits were represented by two appropriate states of a small number of neutral atoms stored in arrays of traps and we provided methods for robust single qubit gates as well as initialisation and measurements of the state of the qubit. Furthermore, we proposed a method for performing two qubit gates via collisional interactions of atoms thus providing a universal set of gates on decoherence free qubits which allowed for arbitrary quantum computations. In order to prove the usefulness and feasibility of these gates with current or near future technology we worked out a scheme for a quantum repeater which represented a complex network of the different quantum operations. A quantum repeater was an important device for quantum communication and its successful implementation would allow for absolutely secure data transfer. We examined in detail the performance of the quantum repeater via analytical calculations and numerical simulations and showed that it could be reliably implemented using our methods. In addition to this, we compared our quantum repeater to a quantum repeater which was built up from conventional, non decoherence-free qubits and showed that it could outperform the latter, meaning that for secure communication over continental or intercontinental distances it could be favourable or even indispensable to use a quantum repeater which would use a technology like the one we developed.

In further parts of our work we pursued another direction to reach the goals of the project. We exploited features of strongly correlated systems consisting of many neutral atoms stored in an array of traps, an optical lattice. The atoms interacted with each other leading to fascinating correlated phenomena which could be used for the purpose of robust quantum information processing. In a first approach we examined a specific many particle system, the quantum Ising model, in a one-dimensional lattice. This system had two energetically equal ground states which represented a robust quantum memory, i.e. it was practically decoherence free.

However, initialisation of and quantum operations on this robust memory required the crossing of a critical point of a quantum phase transition. In our work we gained new insights in the physics of this transition and provided detailed scaling laws for the times which were necessary to perform these operations. This was essential for experimental realisations and so this work was a further contribution towards the implementation of robust quantum memories and quantum information processing.

In another approach, we addressed the problem of providing a quantum register with addressable qubits which was a prerequisite for numerous quantum computing schemes with neutral atoms. We considered the transition from a low density (tonks) gas in a one-dimensional lattice to a commensurately filled lattice (mott insulator) by doubling the lattice periodicity, which was experimentally relatively easy to achieve. The resulting lattice had a large wavelength, i.e. the atoms stored in the different lattice wells -each representing a qubit- had a sufficiently high separation from each other so that they could be individually addressed by an external laser. This was very important since initialisation, readout and single qubit gates could then be performed. We gained insights in this entirely novel quantum transition and also showed that the necessary time scales to create the addressable quantum register were amazingly small, actually significantly smaller than in alternative schemes. The successful implementation of this scheme would significantly contribute to the realisation of reliable quantum information processing.