We give an elementary introduction to the notion of quantum entanglement between distinguishable parties and review a recent proposal about solid state quantum computation with spin-qubits in quantum dots. The indistinguishable character of the electrons whose spins realize the qubits gives rise to further entanglement-like quantum correlations. We summarize recent results concerning this type of quantum correlations of indistinguishable particles.
We give an elementary introduction to the notion of quantum entanglement between distinguishable parties and review a recent proposal about solid state quantum computation with spin-qubits in quantum dots. The indistinguishable character of the electrons whose spins realize the qubits gives rise to further entanglement-like quantum correlations. We summarize recent results concerning this type of quantum correlations of indistinguishable particles.
We briefly review the physics of gate operations between quantum dot spin-qubits and analyze the dynamics of quantum entanglement in such processes. The indistinguishable character of the electrons whose spins realize the qubits gives rise to further entanglement-like quantum correlations that go beyond simple antisymmetrization effects. We also summarize further recent results concerning this type of quantum correlations of indistinguishable particles. Finally we discuss decoherence properties of spin-qubits when coupled to surrounding nuclear spins in a semiconductor nanostructure
Control over electron-spin states, such as coherent manipulation, filtering and measurement promises access to new technologies in conventional as well as in quantum computation and quantum communication. We review our proposal of using electron spins in quantum confined structures as qubits and discuss the requirements for implementing a quantum computer. We describe several realizations of one- and two-qubit gates and of the read-in and read-out tasks. We discuss recently proposed schemes for using a single quantum dot as spin-filter and spin-memory device. Considering electronic EPR pairs needed for quantum communication we show that their spin entanglement can be detected in mesoscopic transport measurements using metallic as well as superconducting leads attached to the dots.
Recent theoretical work on solid-state proposals for the implementation of quantum computation and quantum information processing is reviewed. The differences and similarities between microscopic and macroscopic qubits are highlighted and exemplified by the spin qubit proposal on one side and the superconducting qubits on the other. Before explaining the spin and supercondcuting qubits in detail, some general concepts that are relevant for both types of solid-state qubits are reviewed. The controlled production of entanglement in solid-state devices, the transport of carriers of entanglement, and entanglement detection will be discussed in the final part of this review.
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.
We review our recent work addressing various theoretical issues in spin-based quantum dot quantum computation and quantum information processing. In particular, we summarize our calculation of electron exchange interaction in two-electron double quantum dots and multi-electron double dots, and discuss the physical implication of our results. We also discuss possible errors and how they can be corrected in spin-based quantum dot quantum computation. We critically assess the constraints and conditions required for building spin-based solid state quantum dot quantum computers.
Solid state based quantum information processing is focused on physical implementation of all necessary elements of quantum computation and quantum information in solid state systems, mainly due to their scalability compared to e.g. optical systems. Among many proposals to realize these types of devices, such as quantum dots as charge qubits or Josephson junction circuits, we study here one of the most promising candidates, i.e., the spin of an electron confined to a quantum dot as a qubit. Experimentally, it has been shown that the relaxation rate of this two level system can be pushed above few seconds in low magnetic fields. Moreover, using spin echo techniques, \nthe spin dephasing time can be maximized up to milliseconds with the current technology. This long spin decay time is one of the main reasons that make this system desirable for quantum computation and quantum information purposes. \nWe reexamined the recent measurement based proposal called one-way quantum computation which exploits entanglement and local measurements as tools to perform quantum computation on N qubits. Although it was suggested in the original work to entangle the qubits via the nearest neighbor Ising interaction, we investigated how one can generate the so-called cluster states with the Heisenberg interaction. We extended our method to include more general forms of Heisenberg interaction such as asymmetric coupling of adjacent qubits. These forms of couplings, rather than Ising interaction, are more encountered in solid state devices, and therefore make it possible to perform one-way quantum computation with electron spins in quantum dots coupled via exchange interaction to their adjacent spins. \n \nChapters II, III, and IV of my thesis are devoted to the study of the spin-orbit interaction in heterostructure quantum dots and its effect on the spin dynamics. We observed that one can actually use spin-orbit interaction to manipulate the spin state of an electron on time scales much smaller than the spin dephasing time. Specifically, in chapter II, we studied the effect of a nearby functioning quantum point contact (QPC) on the relaxation of the electron spin and show that the charge fluctuations in QPC lead to spin relaxation of the confined electron in the presence of spin-orbit interactiom and an applied magnetic field. We also addressed the relation of this rate to the microscopic parameters of the system and found some geometrical dependence of the spin relaxation time on the orientation of the QPC on the substrate. Moreover, we showed in chapters III and IV that the spin-orbit interaction can play a positive role, in order to rotate the spin around the Bloch sphere. We considered different mechanisms, particularly, Electron Dipole Spin Resonance (EDSR) and holonomic unitary gates in quantum dots. We verified that these mechanisms of spin manipulation can be realized in solid state systems with the state of the art semiconductor technologies. \n \nChapter V of the thesis covers a slightly different topic and focuses on the role of the Coulomb interaction in electronic transport. There, we reviewed the non-analytic corrections to the Fermi liquid behavior and their consequences on the momentum occupation number of the electrons in a two dimensional electron gas (2DEG). As an example, we calculated the tunneling rate from an interacting electron reservoir onto a quantum dot and compared our result to the corresponding case for electron tunneling between bilayer 2DEGs. Moreover, within RPA approximation, we found that the electron-plasmon coupling leads to a quadratic frequency dependence of the electron self-energy at low frequencies at the Fermi surface. This correction suppresses the same order corrections due to the particle-hole bubble. \n \n \n