In this way general transformations of the quantum state of all the ions can be generated. The ion trap has several features that make this technique promising even though it has only been possible to make a computer with a few qubits, but the upper limit of qubits which can be manipulated with ion traps is unknown. The aim of this part of the programme is to demonstrate fundamental concepts of quantum algorithms with the use of a few quantum bits and, from there on, to push towards experiments with ten quantum bits. In the last couple of years there has been tremendous progress in implementing small NMR quantum computers. It is the aim of the programme to develop NMR computers with three to six qubits in order to investigate algorithms such as quantum error correction and even implementation of Shor's quantum factoring algorithm applied to small numbers.
Many problems arise from the process of building computers with more than three qubits.
The signal from the computer decreases exponentially with the number of qubits, and it becomes difficult to address individual nuclei. Another problem is the inevitable decoherence in NMR experiments that can impose limitations in the number of quantum gates that can be executed on a NMR quantum computer. It is the aim of this part of the network's research to seek to overcome these limitations. Recently, schemes have been proposed to perform quantum logical operations using Josephson junctions. These ideas are based on the dynamics of copper pairs in nanoscale tunnel junctions of a super conducting material.