The goal of this thesis is to investigate theoretically the generation and behaviour of multipartite entanglement for solid-state nanosystems, in particular electron spin quantum bits (so-called 'qubits') in quantum dots. A quantum dot is a tiny potential well where a single electron can be trapped. A quantum bit can be implemented in this system by applying a magnetic field, and thereby lifting the degeneracy of the spin states of the electron. These spins can then be used as single qubits, and engineering many of these quantum dots next to each other gives as a register of qubits. In this scheme, the so-called Loss-DiVincenzo quantum computer, the single spins can be rotated e.g. by applying a time dependent magnetic field, and two spins can interact through controlling the potential barrier between them. A qubit cannot only be in a superposition of the two computational states 0 and 1 at the same time, but an even stranger characteristic arises for multiple qubits: this phenomenon is called entanglement and refers to a strong correlation between two or more qubits, which can not be achieved within the framework of classical physics, and exponentially enlarges the possible states for a N-qubit system as compared to a classical N-bit system. In this thesis we devise algorithms how to generate multipartite entangled states in electron spin qubits in quantum dots. We compare which classes of entangled states can be generated efficiently in this system. Once the states are created, they decay due to a process called decoherence. We compare how entangled states can be generated and detected in a realistic experiment, and which classes of states are the most suitable. Furthermore, we compare which classes conserve the entanglement, and quantify the robustness of various classes of entangled states. In the last chapter, we devise a scheme of how to execute a simple quantum algorithm, the Deutsch-Jozsa algorithm, in a system containing another type of solid-state qubit, the so-called flux qubit.
The goal of this thesis is to investigate theoretically the generation and behaviour of multipartite entanglement for solid-state nanosystems, in particular electron spin quantum bits (so-called 'qubits') in quantum dots. A quantum dot is a tiny potential well where a single electron can be trapped. A quantum bit can be implemented in this system by applying a magnetic field, and thereby lifting the degeneracy of the spin states of the electron. These spins can then be used as single qubits, and engineering many of these quantum dots next to each other gives as a register of qubits. In this scheme, the so-called Loss-DiVincenzo quantum computer, the single spins can be rotated e.g. by applying a time dependent magnetic field, and two spins can interact through controlling the potential barrier between them. A qubit cannot only be in a superposition of the two computational states 0 and 1 at the same time, but an even stranger characteristic arises for multiple qubits: this phenomenon is called entanglement and refers to a strong correlation between two or more qubits, which can not be achieved within the framework of classical physics, and exponentially enlarges the possible states for a N-qubit system as compared to a classical N-bit system. In this thesis we devise algorithms how to generate multipartite entangled states in electron spin qubits in quantum dots. We compare which classes of entangled states can be generated efficiently in this system. Once the states are created, they decay due to a process called decoherence. We compare how entangled states can be generated and detected in a realistic experiment, and which classes of states are the most suitable. Furthermore, we compare which classes conserve the entanglement, and quantify the robustness of various classes of entangled states. In the last chapter, we devise a scheme of how to execute a simple quantum algorithm, the Deutsch-Jozsa algorithm, in a system containing another type of solid-state qubit, the so-called flux qubit.
Nanostructures are promising building blocks for quantum technologies due to their reproducible nature and ability to self-assemble into complex structures. However, the need to control these nanostructures represents a key challenge. Hence, this thesis investigates the manipulation and creation of quantum states in certain nanostructures. The results of this thesis can be applied to quantum information processing and to extremely sensitive magnetic-field measurements.In the first research chapter, we propose and examine methods for entangling two (remote) nuclear spins through their mutual coupling to a transient optically excited electron spin. From our calculations we identify the specific molecular properties that permit high entangling power gates for different protocols.In the next research chapter, we investigate another method to create entanglement; this time between two remote electronic spins. This method uses a very sensitive magnetic-field sensor based on a crystal defect that allows the detection of single magnetic moments. The act of sensing the local field constitutes a two-qubit projective measurement. This entangling operation is remarkably robust to imperfections occurring in an experiment.The third research chapter presents an augmented sensor consisting of a nitrogen-vacancy centre for readout and an `amplifier' spin system that directly senses tiny local magnetic fields. Our calculations show that this hybrid structure has the potential to detect magnetic moments with a sensitivity and spatial resolution far beyond that of a sensor based on only a nitrogen-vacancy centre, and indeed this may be the physical limit for sensors of this class.Finally, the last research chapter investigates measurements of magnetic-field strength using an ensemble of spin-active molecules. Here, we describe a quantum strategy that can beat the common standard strategy. We identify the conditions for which this is possible and find that this crucially depends on the decoherence present in the system.
Nanostructures are promising building blocks for quantum technologies due to their reproducible nature and ability to self-assemble into complex structures. However, the need to control these nanostructures represents a key challenge. Hence, this thesis investigates the manipulation and creation of quantum states in certain nanostructures. The results of this thesis can be applied to quantum information processing and to extremely sensitive magnetic-field measurements.In the first research chapter, we propose and examine methods for entangling two (remote) nuclear spins through their mutual coupling to a transient optically excited electron spin. From our calculations we identify the specific molecular properties that permit high entangling power gates for different protocols.In the next research chapter, we investigate another method to create entanglement; this time between two remote electronic spins. This method uses a very sensitive magnetic-field sensor based on a crystal defect that allows the detection of single magnetic moments. The act of sensing the local field constitutes a two-qubit projective measurement. This entangling operation is remarkably robust to imperfections occurring in an experiment.The third research chapter presents an augmented sensor consisting of a nitrogen-vacancy centre for readout and an `amplifier' spin system that directly senses tiny local magnetic fields. Our calculations show that this hybrid structure has the potential to detect magnetic moments with a sensitivity and spatial resolution far beyond that of a sensor based on only a nitrogen-vacancy centre, and indeed this may be the physical limit for sensors of this class.Finally, the last research chapter investigates measurements of magnetic-field strength using an ensemble of spin-active molecules. Here, we describe a quantum strategy that can beat the common standard strategy. We identify the conditions for which this is possible and find that this crucially depends on the decoherence present in the system.
This thesis discusses various schemes and protocols for quantum information processing in mesoscopic systems with particular focus on using the spin of a particle as the bearer of information. The first chapter introduce various aspects of the field of quantum information used in this thesis such as qubits, entanglement, its quantification, quantum logic gates and entanglement swapping. In this chapter concepts such as AKLT states, decoherence and adiabatic elimination are introduced as they will be relevant in the thesis. In chapter 2 we introduce the Quantum Dots as the solid state system that will primarily be used as the hardware for the development of Quantum Information Processing (QIP). The different properties of quantum dots depending on their size are discussed. The exchange interaction between tunnel coupled quantum dots and the background of quantum computation in quantum dots is described. The principal sources of decoherence and the measurement techniques for spin qubits are presented. In chapter 3, carbon nanowires filled with N@C60 dimers are studied to analyse the entanglement between nuclear spins. The dimer is modelled as a two coupled nuclear spin- electron spin pair with a Heisenberg interaction. The entanglement have been studied depending on the temperature and the intensity of an external magnetic field. Witnessing the entanglement, and particularly bound entanglement are discussed. In chapter 4, the way to extract a singlet from a quantum dot is explored. The system that we model will be consisting of a triple dot and analyse the best way to get the singlet out, with each electron in a separate dot. The chief motivation is to create a singlet between separate dots in a time-scale much faster than that given by spinspin exchange interactions. In chapter 5, quantum logic gates in a triple dot system has been studied. Such gates have been widely studied in double and single quantum dots. Motivated by the advent of experimental set ups of triple dots, we have studied the natural quantum gates that came out of a triple dot system. There are still two spin quantum bits in the three dots and there is an empty intervening dot, which imparts the scheme some advantages, as well as a substantial difference from the class of schemes studied so far. In chapter 6, we model a large square dot. As we describe in chapter 2, the properties of the large dots make them behave with some interesting properties such as hosting Wigner molecules of electrons inside. We explore the application of these structures for quantum information processing. We show here how to get singlet/triplet measurement, entanglement swapping, and how to prepare a 1D AKLT state, using the square dot as a construction block of the system. Finally in chapter 7 conclusions and further work. Here we indicate the further work that could be done with the knowledge present in this thesis and motivated by future advances in the technology.
The computer industry has seen an immense development in the last decades. \nPersonal computers have become available for everybody living in industrialized \ncountries with rapidly increasing performance in terms of speed and storage capacities. \nHowever, the performance of nowadays' computers is fundamentally limited by the \nlaws of classical physics: a classical bit can only take on either of the two distinct \nvalues `0' or `1'. \nIn contrast, a quantum computer could, in principle, make direct use \nof quantum phenomena, such as state superpositions \n-- a quantum bit can be in both states `0' and `1' simultaneously --, \nto perform complex computational tasks much faster than any classical computer. \n \nThe idea of building computers that work according to the laws of quantum physics \nhas opened various fields of research, one of which is the search for the best \nphysical system to use as a quantum bit (qubit). One important criterion for determining \nthe optimal qubit system is the lifetime of state superpositions. \nTypically, once initialized, such superpositions are destroyed on remarkably short \ntimescales due to interactions with the environment -- a process which is referred to \nas decoherence --, posing the question which physical qubit candidate system might show a high-enough robustness against the \ninfluence of the `outside world' to allow for viable quantum computation. \n \nIn this thesis, we will consider three particular realizations of one specific and \nvery promising type of qubit candidate system: \nan electron (or hole) confined to a quantum dot -- a nanoscale structure \nwithin a (typically semiconducting) material --, where the spin states `down' \nand `up' of our electron (or hole) encode the logical states `0' and `1'. \nOur task will be to study the decay of spin-state superpositions in such quantum-dot \nsystems. The main objective of this thesis is to understand the most important physical \nprocesses that lead to spin decoherence and to show ways to suppress this undesirable effect. \nIt turns out that at low temperatures, the main source of decoherence \nis the coupling of the electron (hole) to the surrounding nuclear spins. \n \nThis thesis is divided into three logical parts, corresponding to the three qubit candidate \nsystems under consideration. First we will study electron-spin qubits in III-V semiconductor \nquantum dots, where the electron spin interacts with the nuclear spins of the semiconducting \nhost material \nvia the isotropic Fermi contact hyperfine interaction. Second we consider quantum-dot-confined \nheavy holes and the decoherence of their (pseudo-)spin states due to anisotropic interactions with the \nnuclear spins. Third and last, we study electron-spin qubits made from carbon-nanotube and \ngraphene quantum dots. Quantum dots made of carbon have the advantage of a low abundance \nof spin-carrying nuclear isotopes, therefore reducing decoherence effects significantly. \n \nFor each of the systems under consideration, we will carry out analytical calculations on \nthe nuclear-spin interactions and the spin dynamics of the qubit. Although one main goal of \nthis thesis is to show ways to extend spin decoherence times, we will also focus on physically more \nfundamental questions. Not only the timescale of the decay is relevant for \nthe system's applicability as a qubit, but also the form of the decay which can vary \nsignificantly from system to system. For example, the decay of spin-state superpositions \ncan follow an exponential, super-exponential or power-law decay, and can even pass through \nvarious stages. This is not only of academic interest, but also important for practical \npurposes, such as the implementation of quantum error-correction schemes in a potential \nquantum computer. \n
Spins in a solid-state environment and photons are both promising physical systems regarding the implementation of qubits. Whereas electron and nuclear spins act very well as localized qubits that are able to store and process quantum information, photons are the primary candidates to transmit quantum information between distant locations. Entanglement, on the other hand, is a fundamental resource of quantum information processing enabling, e.g., secure communication over long distances. The generation and manipulation of entanglement are thus fundamental steps in order to leverage the benefits of quantum information processing. The aim of this dissertation is therefore to theoretically investigate entangling mechanisms for various physical systems. A functioning source of entangled photons is a basic hardware component required for quantum communication. To this end, we study a system composed of semiconductor quantum wells inside a microcavity, known as intersubband cavity system, in which the interaction of the electronic system with the cavity field can reach the ultrastrong coupling regime. The ground state contains a finite number of photons, and we find that these photons are entangled. The amount of entanglement is quantified analytically, and maximal entanglement is found to be possible. The technique of entanglement purification allows to restore maximal entanglement that has decreased, e.g. due to decoherence. Purification requires quantum memory, a role for which electron spins in electrically-defined quantum dots are well suited. However, existing purification protocols are rather unpractical in this case. Here, the concept of asymmetric bilateral two-qubit operations is introduced to purify spin entanglement by harnessing the typical interaction between electrons in neighboring quantum dots. As it turns out, this concept can be applied to a variety of qubit systems, e.g. superconducting qubits or spins in nitrogen-vacancy centers in diamond. The latter example offers several possibilities to implement a qubit, of which the intrinsic nitro- gen nuclear spin has proven its viability in many ways. We develop a scheme to deterministically couple two nuclear spin qubits, in which the interaction is mediated by an optical cavity. It is found that an entangling two-qubit gate, also required for universal quantum computation, can be implemented with operation times below 100 nanoseconds, i.e. several orders of magnitude faster compared to the decoherence time of the nuclear spin. The verification of entanglement, which is required e.g. in entanglement-based quantum com- munication to detect an eavesdropping attack, typically involves a measurement of qubit states. Using the input-output formalism, we derive a fully quantum-mechanical model of an optical readout scheme to measure the spin state of an electron in a self-assembled quantum dot.
A two-level quantum system is the building block of a quantum computer. This pair of quantum states defines the computational unit of a quantum computer, and it is called a quantum bit or qubit in analogy to the bit that is the binary unit of a classical computer. The spin of a single electron naturally defines such a two-level quantum system. A quantum dot can be tuned to the single-electron regime, and an array of singly occupied quantum dots provides a multi-qubit register. This thesis describes the multielectron encoding of a spin qubit using a pair or a trio of quantum dots, and it analyzes the coherence properties and manipulation protocols of this system. The singlet-triplet qubit, coded using the singlet state and the spinless triplet state of a pair of singly occupied quantum dots, can be controlled all electrically when applying voltages to gates close to the quantum dot structure. Rapid, subnanosecond modifications of the double quantum dot's charge configuration have been realized successfully. A small magnetic field gradient across the double quantum dot enables universal qubit control. Two modifications of the normal singlet-triplet encoding are introduced. (1) The six-electron configuration of a double quantum dot encodes a singlet-triplet qubit in the same way as for the two-electron double quantum dot. Two electrons at each quantum dot are irrelevant for the qubit manipulations because they are paired in a singlet state; the remaining two electrons encode the qubit. The qubit's wave function is immune to charge noise at moderate out-of-plane magnetic fields. (2) A singlet-triplet qubit encoded using two quantum dots of different sizes has an orbital state degeneracy of the singlet state and the spinless triplet state at finite out-of-plane magnetic fields. Spin-orbit interactions lift this state degeneracy, while the magnitude of the state coupling is determined by the size difference of the QDs. This setup enables the manipulations of singlet-triplet qubits without the need for magnetic field gradients. Finally, two-qubit gates between singlet-triplet qubits are proposed that use mediated exchange interactions via one quantum state. These operations are well controlled and highly noise insensitive. Orbital interactions alone can control spin qubits coded in a three electron Hilbert space. For example, the exchange-only qubit is encoded using three singly occupied quantum dots. The exchange interactions of two quantum dot pairs need to be modified to manipulate this qubit. The noise sensitivity of the exchange-only qubit is discussed. Alternatively, a three-electron qubit at a double quantum dot can be operated when single electrons are transferred between the quantum dots. Fast, subnanosecond manipulations of the double quantum dot's charge configuration are required to realize single-qubit gates. A novel two-qubit pulse gate for the three-electron double quantum dot qubit is proposed.