Andrew M. Steane

Continuous spontaneous localisation (CSL) is a model that captures the effects of a class of extensions to quantum theory which are expected to result from quantum gravity, and is such that wavefunction collapse is a physical process. The rate of such a process could be very much lower than the upper bounds set by searches to date, and yet still modify greatly the interpretation of quantum mechanics and solve the quantum measurement problem. Consequently experiments are sought to explore this. We describe an experiment that has the potential to extend sensitivity to CSL by many orders of magnitude. The method is to detect heating of the motion of charged macroscopic objects confined in a Paul trap. We discuss the detection and the chief noise sources. We find that CSL with standard parameters could be observed using a vibration-isolated ion trap of size 1 cm at ultra-low pressure, with optical interferometric detection.

We demonstrate the use of dynamic decoupling techniques to extend the coherence time of a single memory qubit by nearly two orders of magnitude. By extending the Hahn spin-echo technique to correct for unknown, arbitrary polynomial variations in the qubit precession frequency, we show analytically that the required sequence of pi-pulses is identical to the Uhrig dynamic decoupling (UDD) sequence. We compare UDD and CPMG sequences applied to a single Ca-43 trapped-ion qubit and find that they afford comparable protection in our ambient noise environment.

Experimental methods for laser-control of trapped ions have reached sufficient maturity that it is possible to set out in detail a design for a large quantum computer based on such methods, without any major omissions or uncertainties. The main features of such a design are given, with a view to identifying areas for study. The machine is based on 13000 ions moved via 20 micron vacuum channels around a chip containing 160000 electrodes and associated classical control circuits; 1000 laser beam pairs are used to manipulate the hyperfine states of the ions and drive fluorescence for readout. The computer could run a quantum algorithm requiring 10^9 logical operations on 300 logical qubits, with a physical gate rate of 1 MHz and a logical gate rate of 8 kHz, using methods for quantum gates that have already been experimentally implemented. Routes for faster operation are discussed.

The "pushing gate" proposed by Cirac and Zoller in 2000 for quantum logic in ion traps is discussed, in which a force is used to give a controlled push to a pair of trapped ions and thus realize a phase gate. The original proposal had a weakness in that it involved a hidden extreme sensitivity to the size of the force. Also, the physical origin of this force was not fully addressed. Here, we discuss the sensitivity and present a way to avoid it by choosing the spatial form of the pushing force in an optimal way. We also analyse the effect of imperfections in a pair of pi pulses which are used to implement a "spin-echo" to cancel correlated errors. We present a physical model for the force, namely the dipole force, and discuss the impact of unwanted photon scattering, and of finite temperature of the ions. The main effect of the temperature is to blur the phase of the gate owing to the ions exploring a range of values of the force. When the distance scale of the force profile is smaller than the ion separation, this effect is more important than the high-order terms in the Coulomb repulsion which were originally discussed. Overall, we find that whereas the "pushing gate" is not as resistant to imperfections as was supposed, it remains a significant candidate for ion trap quantum computing since it does not require ground state cooling, and in some cases it does not require the Lamb-Dicke limit, while the gate rate is fast, close to (rather than small compared to) the trap vibrational frequency.

An introductory review of the linear ion trap is given, with particular regard to its use for quantum information processing. The discussion aims to bring together ideas from information theory and experimental ion trapping, to provide a resource to workers unfamiliar with one or the other of these subjects. It is shown that information theory provides valuable concepts for the experimental use of ion traps, especially error correction, and conversely the ion trap provides a valuable link between information theory and physics, with attendant physical insights. Example parameters are given for the case of calcium ions. Passive stabilisation will allow about 200 computing operations on 10 ions; with error correction this can be greatly extended.