This thesis describes experimental work in which the spin and motional states of one and two trapped atomic ions are manipulated with long-wavelength radiation in the microwave and radio frequency (RF) regime. This allows single- and two-qubit quantum logic gates to be implemented with long-wavelength radiation, in contrast to laser frequency radiation used in the majority of work to date. The two-qubit gate scheme developed represents a significant advance towards a large scale quantum computing architecture in which laser light is not needed for coherent manipulation. An experimental setup is built in which a macroscopic linear Paul trap is fitted with permanent magnets to create a strong axial magnetic field gradient. This addition allows the spin and motional states of the ions to be coupled using long-wavelength radiation. The coherence time of qubits that are sensitive to the magnetic field gradient is increased by nearly three orders of magnitude with the use of dressed states and the lifetime and coherence time are measured to be T1 = 0.63(4) s and T2 = 0.65(5) s, respectively. Using the dressed-state qubit, sideband cooling of a single ion to the motional ground state is demonstrated, and the final mean phonon number after cooling is measured to be \bar{n} = 0.13(4). Finally, a two-qubit gate is demonstrated using the dressed-state qubits in conjunction with the magnetic field gradient, and a Bell state fidelity of F = 0.985(12) is determined. This is a significant increase in fidelity for a two-qubit gate based on long-wavelength radiation compared to previous work. The errors are analysed and it is shown that with the next generation of microfabricated traps being developed in the group, the gate fidelity using this scheme can be pushed far into the fault tolerant regime. This makes this scheme promising as an integral part of a large scale quantum computing architecture.
This thesis describes experimental work in which the spin and motional states of one and two trapped atomic ions are manipulated with long-wavelength radiation in the microwave and radio frequency (RF) regime. This allows single- and two-qubit quantum logic gates to be implemented with long-wavelength radiation, in contrast to laser frequency radiation used in the majority of work to date. The two-qubit gate scheme developed represents a significant advance towards a large scale quantum computing architecture in which laser light is not needed for coherent manipulation. An experimental setup is built in which a macroscopic linear Paul trap is fitted with permanent magnets to create a strong axial magnetic field gradient. This addition allows the spin and motional states of the ions to be coupled using long-wavelength radiation. The coherence time of qubits that are sensitive to the magnetic field gradient is increased by nearly three orders of magnitude with the use of dressed states and the lifetime and coherence time are measured to be T1 = 0.63(4) s and T2 = 0.65(5) s, respectively. Using the dressed-state qubit, sideband cooling of a single ion to the motional ground state is demonstrated, and the final mean phonon number after cooling is measured to be \bar{n} = 0.13(4). Finally, a two-qubit gate is demonstrated using the dressed-state qubits in conjunction with the magnetic field gradient, and a Bell state fidelity of F = 0.985(12) is determined. This is a significant increase in fidelity for a two-qubit gate based on long-wavelength radiation compared to previous work. The errors are analysed and it is shown that with the next generation of microfabricated traps being developed in the group, the gate fidelity using this scheme can be pushed far into the fault tolerant regime. This makes this scheme promising as an integral part of a large scale quantum computing architecture.
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.
In this thesis, I discuss coherent manipulation of a trapped ytterbium ion using long wavelength radiation and the results of experiments towards the performance of a two-ion entanglement gate using a static magnetic field gradient of 23.3(6) T/m to create coupling between an ion's internal state and its motion. After using these experiments to explain the requirements for high-fidelity entanglement operations, I continue by examining existing methods for creating this gradient, the current limiting factor in producing the highest fidelity operations. This includes a full characterisation of the gradients produced by symmetric scheme permanent magnets and buried current carrying wires including development of scaling laws in order to create optimum gradients for a given trap geometry. I continue by proposing a new method by which extremely high gradients over 100 T/m can be created for planar chip traps with minimal modification to an existing experiment. These gradients are tailored for axial as well as radial entanglement schemes and aim to show that the technology exists in order to produce a two-qubit gate over the fault tolerant threshold. Subsequently, I discuss the implementation of this new scheme in an experiment before constructing the apparatus to accurately align a chip with these magnets and documenting their installation into two new experimental setups. This includes a preliminary measurement of the gradient produced by an imperfect setup outside of vacuum which verifies those simulated at ~ 110 T/m. Lastly, I discuss the prospects of on-chip magnetic materials and propose a new method which when sufficiently developed should allow for high magnetic field gradients to be produced on-chip at higher ion heights than when solely using current carrying wires. Additionally this scheme should allow for switchable gradients with maximised stability in geometries previously not possible to create.
Scalability is a challenging yet key aspect required for large scale quantum computing and simulation using ions trapped in radio-frequency (rf) Paul traps. In this thesis 171Yb+ ions are used to demonstrate a magnetic field insensitive qubit which has a measured coherence time of 1.5 s, making it an ideal candidate to use for storing quantum information. A magnetic field sensitive qubit is also characterised which can be used for the implementation of multi-qubit gates using a potentially very scalable scheme based on microwaves in conjunction with a static magnetic field gradient instead of using lasers. However, the measured coherence time is limited by magnetic field fluctuations and will prohibit high fidelity gate operations from being performed. To address this issue, the preparation of a dressed-state qubit using a microwave based stimulated rapid adiabatic passage (STIRAP) pulse sequence will be presented. This qubit is protected against the noisy environment making it less sensitive to magnetic field fluctuations. The lifetime of this qubit is measured to demonstrate its suitability for storing quantum information. A powerful method for manipulating the dressed-state qubit will be presented and is used to measure a coherence time of the qubit of 500 ms which is two orders of magnitude longer compared to the magnetic field sensitive qubit. It will also be shown that our method allows for the implementation of arbitrary rotations of the dressed-state qubit on the Bloch sphere using only a single rf field. This substantially simplifies the experimental setup for single and multi-qubit gates. Furthermore, this thesis will present a experimental setup capable of successfully operating microfabricated surface ion traps. This setup is then used to operate and characterise the first two-dimensional (2D) lattice of ion traps on a microchip. A unique feature of the microfabrication technique used for this device is the extremely large voltage that can be applied which allows long ion lifetimes along with large secular frequencies to be measured, demonstrating the robustness of this device. Rudimentary shuttling between neighbouring lattice sites will be shown which could be used as part of a efficient scheme to load a large lattice of ions. One of the many applications of a 2D lattice of ions lies in the field of quantum simulations where many-body systems such as quantum magnetism, high temperature superconductivity, the fractional quantum hall effect and synthetic gauge fields can be simulated. It will be shown how making only minor modifications to the microchip the ion-ion separation can be reduced sufficiently to offer an exciting platform for the successful implementation of 2D quantum simulations. A theoretical investigation on the optimal 2D ion trap lattice geometry will also be presented with the aim to maximise the ratio of ion-ion coupling strength to decoherence from motional heating of the ions and to laser induced off-resonant coupling.
This thesis describes experimental work towards the development of a trapped-ion quantum computer based on microchip ion traps and long-wavelength radiation, using magnetic field gradients. The relationship between experimental parameters and two-qubit gate fidelity is investigated for microchips with two different static magnetic field gradient generation methods. For current-carrying wires and under-chip permanent magnets, optimum ion heights of 110 μm and 200 μm are found respectively. Construction of an experiment capable of demonstrating high-fidelity gates is reported, including innovations for the use of microchip ion traps with permanent magnets. The development of a vacuum system for versatile microchip experiments is described, including new methods for impedance-matched RF delivery, in-vacuum filtering and liquid nitrogen microchip cooling. Protection of both the microchip surface from atomic flux and of ions from the charged imaging viewport are both investigated in detail. A new preparation framework for microchip ion traps before their use in experiments is developed. In order to remove unwanted deposited layers on the microchips, a process of multiple chemical treatments is used. In addition, these characterisation efforts lead to refinement of the microfabrication process for future microchips. The application of large currents to microchips is of fundamental importance to scalable trapped-ion quantum computing using static magnetic field gradients. As part of the characterisation process, currents of ≈ 10A are successfully applied to microfabricated current-carrying wires, demonstrating the viability of these structures for generation of local magnetic fields and gradients in a quantum computing device. The operation of a microchip ion trap experiment with under-chip permanent magnets for a high magnetic field gradient (≈ 140Tm−1) is described. The successful trapping of ytterbium-174 and -171 ions is reported, as well as their use to measure and optimise the ion trap parameters. The thesis concludes with consideration of the expected future results from the ongoing operation of the experiment.
Quantum computers offer great potential for significant speedup in executing certain algorithms compared to their classical counterparts. One of the most promising physical systems in which implementing such a device seems viable are trapped atomic ions. All of the fundamental operations needed for quantum information processing have already been experimentally demonstrated in trapped ion systems. Today, the remaining two obstacles are to improve the fidelities of these operations up to the point where quantum error correction techniques can be successfully applied, as well as to scale up the present systems to a higher number of quantum bits (qubits). This thesis addresses both issues. On the one hand, it decribes the experimental implementation of a high-fidelity two-qubit quantum logic gate, which is the most technically demanding fundamental operation to realise in practice. On the other hand, the presented work is carried out in a microfabricated surface ion trap – an architecture that holds the promise of scalability. The gate is applied directly to hyperfine "atomic clock" qubits in 43Ca+ ions using the near-field microwave magnetic field gradient produced by an integrated trap electrode. To protect the gate against fluctuating energy shifts of the qubit states, as well as to avoid the need to null the microwave field at the position of the ions, a dynamically decoupled Mølmer-Sørensen scheme is employed. After accounting for state preparation and measurement errors, the achieved gate fidelity is 99.7(1)%. In previous work, the same apparatus has been used to demonstrate coherence times of T*2 ≈ 50 s and all single-qubit operations with fidelity > 99.95%. To gain access to the "atomic clock" qubit transition in 43Ca+, a static magnetic field of 146G is applied. The resulting energy level Zeeman-structure is spread over many times the linewidth of the atomic transition used for Doppler cooling. This thesis presents a simple and robust method for Doppler cooling and obtaining high fluorescence from this qubit in spite of the complicated level structure. A temperature of 0.3mK, slightly below the Doppler limit, is reached.
For quantum computers to become a reality, high-fidelity logic gates are required to be implemented on a scalable architecture. The IQT group follows an approach based on using a magnetic field gradient and microwave radiation to implement the required operations. To demonstrate their scalability to many quantum bit systems, these operations need to be implemented on micro-fabricated surface ion traps. In this thesis I describe the technologies I developed for surface ion traps with magnetic field gradients. This entailed the design, assembly and operation of two surface ion trap systems with permanent magnets for generating large magnetic field gradients of 140T=m, novel in-vacuum radio-frequency and microwave emitters for implementing high-speed quantum state manipulation and development of robust and reliable laser control systems required for stable long-term experimental operation.