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Microwave-based controlled quantum dynamics in trapped ions

Gatis Mikelsons

Published Dec 1, 2014• 0 citations
Publisher

Abstract

The key research aim of the present thesis is the building of a universal set of quantum gates for a long wavelength trapped-ion quantum information processor. It is desired to realise quantum computation using microwave and radio wave sources in a linear ion trap, where a static magnetic field gradient has been added to enhance motional and atomic state coupling. Furthermore, the qubit is constructed with the intrinsic use of superposition states generated with the help of constant microwave fields in the background: dressed states. This technique is essential for the shielding of the quantum operations against the unavoidable effects of magnetic noise. After reviewing the preliminary results and discussing briefly an auxiliary experimental technique intrinsic to the set-up, we introduce the magnetic gradient coupling and the dressed state scheme. We then proceed to illustrate how single and multi-qubit gates can be realised within such a system. Theoretical arguments are supplemented by numerical simulation and sources of experimental noise are taken into account.

DOI
10.25560/25336

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The key research aim of the present thesis is the building of a universal set of quantum gates for a long wavelength trapped-ion quantum information processor. It is desired to realise quantum computation using microwave and radio wave sources in a linear ion trap, where a static magnetic field gradient has been added to enhance motional and atomic state coupling. Furthermore, the qubit is constructed with the intrinsic use of superposition states generated with the help of constant microwave fields in the background: dressed states. This technique is essential for the shielding of the quantum operations against the unavoidable effects of magnetic noise. After reviewing the preliminary results and discussing briefly an auxiliary experimental technique intrinsic to the set-up, we introduce the magnetic gradient coupling and the dressed state scheme. We then proceed to illustrate how single and multi-qubit gates can be realised within such a system. Theoretical arguments are supplemented by numerical simulation and sources of experimental noise are taken into account.
We propose a set of techniques that enable universal quantum computing to be carried out using dressed states. This applies in particular to the effort of realizing quantum computation in trapped ions using long-wavelength radiation, where coupling enhancement is achieved by means of static magnetic-field gradient. We show how the presence of dressing fields enables the construction of robust single and multi-qubit gates despite the unavoidable presence of magnetic noise, an approach that can be generalized to provide shielding in any analogous quantum system that relies on the coupling of electronic degrees of freedom via bosonic modes.
Abstract We propose a set of techniques that enable universal quantum computing to be carried out using dressed states. This applies in particular to the effort of realizing quantum computation in trapped ions using long-wavelength radiation, where coupling enhancement is achieved by means of static magnetic-field gradient. We show how the presence of dressing fields enables the construction of robust single and multi-qubit gates despite the unavoidable presence of magnetic noise, an approach that can be generalized to provide shielding in any analogous quantum system that relies on the coupling of electronic degrees of freedom via bosonic modes.
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 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.
This thesis describes the experimental work towards the development of a scalable quantum computer based on microfabricated ion trap using long-wavelength radiation and magnetic field gradient. There are three key elements in implementing such a quantum computer: the junction trap to shuttle ions, the structure to generate high gradient magnetic field and the structure to induce strong microwave coupling to the ions. A new dynamic simulation tool was developed addressing the problems faced by static solvers. This tool was used to aid the design and optimisation of an X junction geometry allowing the ions to be shuttled with minimised motional heating gain. The design and fabrication techniques were reported on the structure to generate a high gradient magnetic field. A discussion was given on the design of producing microwave and maximise the coupling to the cold ions. A review was given on the far-field methods and near-field methods. A novel design was reported where the single-qubit gate is predicted to be 45 times faster than a conventional setup. Two essential topics on the microfabrication of a reliable scalable quantum computer unit were discussed: breakdown and RF loss. Investigation using numerical simulations showed that dielectric can breakdown due to high voltage and local heating which are results of impedance mismatch. Microfabrication processes were improved, high-quality films were reported to have twice as much breakdown voltages. The mechanisms of RF loss were reviewed. Novel structures and smooth electroplating technique were developed to minimise the loss. A low loss ion trap was produced and tested. An experimentally observed anomalous glow discharge phenomenon was reported and investigated.
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.