S. Bose

Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible logic gates built from the coherent dynamics of a few interacting atoms. As superpositions are unnecessary before and after each such gate (inputs and outputs are bits), the dephasing time only needs to exceed a single gate operation time, while fault tolerance should be achieved with low overhead, by classical coding. Such gates could thus be a spin-off of quantum technology much before full-scale quantum computation. Thus motivated, we propose methods to realize the 3-bit Toffoli and Fredkin gates universal for classical reversible logic using a single time-independent 3-qubit Hamiltonian with realistic nearest neighbour two-body interactions. We also exemplify how these gates can be composed to make a larger circuit. We show that trapped ions may soon be scalable simulators for such architectures, and investigate the prospects with dopants in silicon.

We study two trapped ions coupled to the axial phonon modes of a one-dimensional Coulomb crystal. This system is formally equivalent to the "two spin-boson" model. We propose a scheme to dynamically generate a maximally entangled state of two ions within a decoherence-free subspace. Here the phononic environment of the trapped ions, whatever its temperature and number of modes, serves as the entangling bus. The efficient production of the pure singlet state can be exploited to perform short-ranged quantum communication which is essential in building up a large-scale quantum computer.

Quantum information processing rests on our ability to manipulate quantum superpositions through coherent unitary transformations, and to establish entanglement between constituent quantum components of the processor. The quantum information processor (a linear ion trap, or a cavity confining the radiation field for example) exists in a dissipative environment. We discuss ways in which entanglement can be established within such dissipative environments. We can even make use of a strong interaction of the system with its environment to produce entanglement in a controlled way.

We propose a scheme for measuring the Berry phase in the vibrational degree of freedom of a trapped ion. Starting from the ion in a vibrational coherent state we show how to reverse the sign of the coherent state amplitude by using a purely geometric phase. This can then be detected through the internal degrees of freedom of the ion. Our method can be applied to preparation of Schrödinger cat states.

Quantum information processing rests on our ability to manipulate quantum superpositions through coherent unitary transformations. In reality the quantum information processor (a linear ion trap, or cavity qed implementation for example) exists in a dissipative environment. Dephasing, and other technical sources of noise, as well as more fundamental sources of dissipation severely restrict quantum processing capabilities. The strength of the coherent coupling needed to implement quantum logic is not always independent of dissipation. The limitations these dissipative influences present will be described and the need for efficient error correction noted. Even if long and involved quantum computations turn out to be hard to realize, one can perform interesting manipulations of entanglement involving only a few gates and qubits, of which we give examples. Quantum communication also involves manipulations of entanglement which are simpler to implement than elaborate computations. We briefly analyse the notion of the capacity of a quantum communication channel.