The ability to control the evolution of quantum systems would open the door to a new world of information processing. Nuclear spin qubits in the solid state offer the longest coherence times, of the order of a few seconds, however their initialization, readout and coupling are yet to be demonstrated. This thesis addresses the physical manipulation of nuclear spin qubits with a classical electric current. Our main result is the development of a mechanism that provides high contrast initialization and readout of nuclear spin qubits using their interaction with conduction electrons. However, we also show that conduction electrons can not be used to entangle nuclear spin qubits without destroying the nuclear spin qubit coherence. We show this by demonstrating that the quality factor of a Ruderman-Kittel-Kasuya-Yosida (RKKY) gate is always low for electron as well as nuclear spin qubits. In conclusion, we establish the viability of a quantum computer architecture based on nuclear spins that relies on conduction electrons for quantum read-out and initial- ization. For coherent entanglement, we argue that the usual direct exchange interac- tion is still the best option. / Graduate

Konstanz, Univ., Diplomarb., 2006.

In this thesis I present a theory of a macroscopic singlet-triplet qubit in quantum dots embedded in nanowires, each containing 4 electrons and together simulating an artficial Haldane gap material. A Haldane gap material exhibits a 4-fold degenerate ground state separated by an energy gap from excitations. The ground state is equivalent to a degenerate spin-singlet and -triplet state. The 4 degenerate states exhibit the characteristics of spins-1/2 localized on either end of the chain. These states may be used as a coded qubit for quantum information processing. Using the effective mass approximation, I calculate single-particle energy levels of one and two quantum dots in a quantum wire. Using these energy levels I compute the Coulomb matrix elements of the interacting Hamiltonian. Using configuration interaction I demonstrate that the ground state of a quantum dot with 4 electrons is a spin-1 state. I then show that the two dot system behaves approximately like two spin-1 objects interacting via an antiferromagnetic Heisenberg Hamiltonian. While the Heisenberg model is approximate, the two dots have a spin-0 ground-state, indicating antiferromagnetic coupling. I then present a simpler spin model to illustrate the physical parameters which control this interaction. Finally, I present a brief solution to the Heisenberg Hamiltonian for finite spin-chains, and show how one can manipulate the singlet-triplet combined ground state of the spin-chain via localized magnetic field, realizing a singlet-triplet qubit in a macroscopic semiconductor device.

Modelling of phosphorus donor-based silicon (Si:P) qubit devices and mesoscopic single-electron devices is presented in this thesis. This theoretical analysis is motivated by the use of Si:P devices for scalable quantum computing. Modelling of Si:P single-electron devices (SEDs) using readily available simulation tools is presented. The mesoscopic properties of single and double island devices with source-drain leads is investigated through ion implantation simulation (using Crystal-TRIM), 3D capacitance extraction (FastCap) and single-electron circuit simulation (SIMON). Results from modelling two generations of single and double island Si:P devices are given, which are shown to accurately capture their charging behaviour. The trends extracted are used to forecast limits to the reduction in size of this Si:P architecture. Theoretical analysis of P2+:Si charge qubits is then presented. Calculations show large ranges for the SET measurement signal, Δq, and geometric ratio factor, α, are possible given the 'top-down' fabrication procedure. The charge qubit energy levels are calculated using the atomistic simulator NEMO 3-D coupled to TCAD calculations of the electrostatic potential distribution, further demonstrating the precise control required over the position of the donors. Theory has also been developed to simulate the microwave spectroscopy of P2+:Si charge qubits in a decohering environment using Floquet theory. This theory uses TCAD finite-volume modelling to incorporate realistic fields from actual device gate geometries. The theory is applied to a specific P2+:Si charge qubit device design to study the effects of fabrication variations on the measurement signal. The signal is shown to be a sensitive function of donor position. Design and analysis of two different spin qubit architectures concludes this thesis. The first uses a high-barrier Schottky contact, SET and an implanted P donor to create a double-well suitable for implementation as a qubit. The second architecture is a MOS device that combines an electron reservoir and SET into a single structure, formed from a locally depleted accumulation layer. The design parameters of both architectures are explored through capacitance modelling, TCAD simulation, tunnel barrier transmission and NEMO 3-D calculations. The results presented strengthen the viability of each architecture, and show a large Δq (> 0.1e) can be expected.

Modelling of phosphorus donor-based silicon (Si:P) qubit devices and mesoscopic single-electron devices is presented in this thesis. This theoretical analysis is motivated by the use of Si:P devices for scalable quantum computing. Modelling of Si:P single-electron devices (SEDs) using readily available simulation tools is presented. The mesoscopic properties of single and double island devices with source-drain leads is investigated through ion implantation simulation (using Crystal-TRIM), 3D capacitance extraction (FastCap) and single-electron circuit simulation (SIMON). Results from modelling two generations of single and double island Si:P devices are given, which are shown to accurately capture their charging behaviour. The trends extracted are used to forecast limits to the reduction in size of this Si:P architecture. Theoretical analysis of P2+:Si charge qubits is then presented. Calculations show large ranges for the SET measurement signal, Δq, and geometric ratio factor, α, are possible given the 'top-down' fabrication procedure. The charge qubit energy levels are calculated using the atomistic simulator NEMO 3-D coupled to TCAD calculations of the electrostatic potential distribution, further demonstrating the precise control required over the position of the donors. Theory has also been developed to simulate the microwave spectroscopy of P2+:Si charge qubits in a decohering environment using Floquet theory. This theory uses TCAD finite-volume modelling to incorporate realistic fields from actual device gate geometries. The theory is applied to a specific P2+:Si charge qubit device design to study the effects of fabrication variations on the measurement signal. The signal is shown to be a sensitive function of donor position. Design and analysis of two different spin qubit architectures concludes this thesis. The first uses a high-barrier Schottky contact, SET and an implanted P donor to create a double-well suitable for implementation as a qubit. The second architecture is a MOS device that combines an electron reservoir and SET into a single structure, formed from a locally depleted accumulation layer. The design parameters of both architectures are explored through capacitance modelling, TCAD simulation, tunnel barrier transmission and NEMO 3-D calculations. The results presented strengthen the viability of each architecture, and show a large Δq (> 0.1e) can be expected.

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.

As systems/structures get smaller we need to take into account noise and quantum effects and so, we need to develop some quantum devices. Quantum devices work using quantum principles like qubits that have already been developed, i.e., superconducting qubits that are going to be discussed in chapter 1. Initially, scientists wanted to use qubits to do quantum computations, this is not easy so scientists developed methods to do something different, e.g. quantum metamaterials. Here in this thesis we describe two examples of quantum devices. Our first device is the parametric quantum amplifier. Used when we need to amplify very weak signals. Amplifying a weak signal on the nanoscale is a very big challenge, this is due to classical and quantum noise, and so, we need to employ quantum physics to resolve this issue. The proposed two-qubit system amplifies weak signals at very small scales. We have shown that we can construct a multitude of novel devices on the nano-scale with the use of qubits Our second device uses harmonic mixing. It can be used where rectification is needed, for example, when we need to rectify some fluctuations and in principle some quantum fluctuations in order to pump either an excited or ground state of the two qubit device. In this thesis we propose how to do this. Firstly, we propose that if we apply harmonic mixing of two signals for two qubits, using the structure of the equation and basically the structure of quantum mechanics we can pump a desirable quantum state. We can pump either the upper or ground state by changing the signal.

Conventional computing based on classical technologies is approaching its limits. Therefore scientists are starting to consider the applications of quantum mechanics as a means for constructing more powerful computers. After proposing theoretical methods, many experimental setups have been designed to achieve quantum computing in reality. This thesis gives some background information on the subject of quantum computing. We first review the concept of quantum entanglement, which plays a key role in quantum computing, and then we discuss the physics of the SQUIDs-cavity method proposed by Yang et al., and give the definitions of quantum gates which are the elements that are needed to construct quantum circuits. Finally we give an overview of recent developments of SQUIDs-cavity systems and quantum circuits after Yang et al.'s proposal in 2003. These new developments help to take a step towards the constructions of higher levels of quantum technologies, e.g. quantum algorithms and quantum circuits.

Zugl.: Karlsruhe, Univ., Diss., 2007

Augsburg, Univ., Diss., 2008