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Kluwer Academic Publishers eBooks

Quantum Computation with “Hot” Trapped Ions

Daniel F. V. James, Sara Schneider, Gerard J Milburn

Published Dec 19, 2005• 3 citations
Publisher

Abstract

We describe two methods that have been proposed to circumvent the problem of heating by external electromagnetic fields in ion trap quantum computers. Firstly the higher order modes of ion oscillation (i. e. modes other than the center-of-mass mode) have much slower heating rates, and can therefore be employed as a reliable quantum information bus. Secondly we discuss a recently proposed method combining adiabatic passage and a number-state dependent phase shift which allows quantum gates to be performed using the center-of-mass mode as the information bus, regardless of its initial state. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/0-306-47097-7_38

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We describe two methods that have been proposed to circumvent the problem of heating by external electromagnetic fields in ion trap quantum computers. Firstly the higher order modes of ion oscillation (i. e. modes other than the center-of-mass mode) have much slower heating rates, and can therefore be employed as a reliable quantum information bus. Secondly we discuss a recently proposed method combining adiabatic passage and a number-state dependent phase shift which allows quantum gates to be performed using the center-of-mass mode as the information bus, regardless of its initial state. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We propose the efficient combinations of laser pulses for constructing a multiqubit gate with cold trapped ions in order to implement maximally entangled states with quantum logic. Within the ion-trap quantum computation using the center of mass as the data bus, we can minimize the number of laser pulses as well as their operation time, which can improve the fidelity. We also present some numerical results of the operation time for different numbers of qubits and values of the Lamb-Dicke parameter.
This thesis is concerned with various aspects of ion traps and their use as a quantum simulation and computation device. In its first part we investigate various sources of noise and decoherence in ion traps. As quantum information is very fragile, a detailed knowledge of noise and decoherence sources in a quantum computation device is essential. In the special case of an ion trap quantum computer we investigate the effects of intensity and phase noise in the laser, which is used to perform the gate operations. We then look at other sources of noise which are present without a laser being switched on. These are fluctuations in the trapping frequency caused by noise in the electric potentials applied to the trap and fluctuating electrical fields which will cause heating of the centre-of-mass vibrational state of the ions in the trap. For the case of fluctuating electrical fields we estimate the effect on a quantum gate operation. We then propose a scheme for performing quantum gates without having the ions cooled down to their motional ground state. The second part deals with various aspects of the use of ion traps as a device for quantum computation. We start with the use of ionic qubits as a measurement device for the centre-of-mass vibrational mode and investigate in detail the effect these measurements will have on the vibrational mode. If one wants to use quantum computation devices as systems to simulate quantum mechanics, it is of interest to know how to simulate say a k-level system with N qubits. We investigate the easiest case of this wider problem and look at how to simulate a three-level system (a so called trit) with two qubits in an ion trap quantum computer. We show how to get and measure a SU (3) geometric phase with this toy model. Finally we investigate how to simulate collective angular momentum models with a string of qubits in an ion trap. We assume that the ionic qubits are coupled to a thermal reservoir and derive a master equation for this case. We investigate the semiclassical limit of this master equation and, in the case for two qubits in the trap, determine the entanglement of the steady state. We also outline a way to find the steady state for the master equation using coherence vectors.
This thesis describes experimental work on implementing single and two qubit gates in ¹7¹Yb+ ions using methods suitable for a large scale quantum computer. By combining a magnetic field gradient with microwave and radiofrequency radiation, the spin and motional states of the ions are coupled which allows multi-qubit operations to be performed, as well as providing individual addressing of ions in frequency space. A dressed state qubit is used which exhibits an increase of over two orders of magnitude in the coherence time for a qubit that it is sensitive to the magnetic field gradient. Using this system, single qubit gates are characterised using the technique of randomised benchmarking, resulting in a measured average error per gate of 9(3)x10¯4. A new type of two qubit gate is experimentally demonstrated, which in comparison to a standard two qubit gate shows significantly increased resilience to two major sources of gate infidelity: heating of the motional mode of the ions during gate operations, and incorrectly set gate field frequencies. These types of errors are expected to become increasingly important with the move towards quantum processors with large numbers of qubits. Using this same technique, a two qubit gate is also demonstrated at a higher initial temperature with a significantly improved fidelity compared to standard methods. These gate techniques are used to demonstrate work towards implementing positiondependent quantum logic, a method which could remove the correlation between the number of ions and the number of gate fields required in a large scale quantum computing architecture. A method to move the dressed state qubit through a magnetic field gradient while preserving quantum information is demonstrated, as well as a method to optimise the phase of a two qubit gate of unknown phase in order to implement a CNOT logic gate. This provides a path forwards to demonstrating a CNOT gate using position-dependent quantum logic.
We describe two schemes to manipulate the electronic qubit states of trapped ions independent of the collective vibrational state of the ions. The first scheme uses an adiabatic method, and thus is intrinsically slow. The second scheme takes the opposite approach and uses fast pulses to produce an effective direct coupling between the electronic qubits. This last scheme enables the simulation of a number of nonlinear quantum systems including systems that exhibit phase transitions, and other semiclassical bifurcations. Quantum tunnelling and entangled states occur in such systems.