5 

Entanglement in SolidState Nanostructures
The goal of this thesis is to investigate theoretically the generation and behaviour of multipartite entanglement for solidstate nanosystems, in particular electron spin quantum bits (socalled '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 socalled LossDiVincenzo 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 Nqubit system as compared to a classical Nbit 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 DeutschJozsa algorithm, in a system containing another type of solidstate qubit, the socalled flux qubit.

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8 

Interqubit coupling mediated by a highexcitationenergy quantum object
We consider a system composed of two qubits and a high excitation energy quantum object used to mediate coupling between the qubits. We treat the entire system quantum mechanically and analyze the properties of the eigenvalues and eigenstates of the total Hamiltonian. After reproducing well known results concerning the leading term in the mediated coupling, we obtain an expression for the residual coupling between the qubits in the off state. We also analyze the entanglement between the three objects, i.e., the two qubits and the coupler, in the eigenstates of the total Hamiltonian. Although we focus on the application of our results to the recently realized parametriccoupling scheme with two qubits, we also discuss extensions of our results to harmonicoscillator couplers, couplers that are near resonance with the qubits and multiqubit systems. In particular, we find that certain errors that are absent for a twoqubit system arise when dealing with multiqubit systems.

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10 

Faulttolerant architectures for nanoelectronic and quantum devices
The progress in CMOS technology has entered the submicron realm, and the technology will approach its limits within about 15 years. Already various novel information processing devices, based on quantum mechanical effects at the nanometer scale, have been widely investigated and some have been successfully demonstrated at the circuit level. This advance in nanoelectronic devices has also motivated efforts in the research of nanoelectronic and quantum computer architectures. Due to the components' poor reliabilities, these architectures will have to be robust against device and interconnect failures. In order to avoid power dissipation problems, the components will have to be applied in the quantum mechanical domain, while due to potential problems in interconnects, the components should be locally interconnected only.
This dissertation is devoted to pursuing solutions to architectural issues that come up when designing a nanoelectronic computer. It explores the possibility of building viable and reliable computer systems from novel nanoelectronic and quantum devices. In particular, parallel processor architectures that are faulttolerant and locallycoupled have been researched.
Chapter 1 presents an introduction to the issues that play a role in nanoelectronics, in contrast with microelectronics, and discusses implications for nanocomputer architectures.
A brief review of the current status in nanoelectronics and recent progress in nanoarchitecture research is presented in Chapter 2.
Chapter 3 describes research on faulttolerant architectures. We review von Neumann's NAND multiplexing technique and extended his study from a high degree of redundancy to a fairly low degree of redundancy. We show the stochastic Markovian nature of a multistage multiplexing system and work out its characteristics. We develop a system architecture based on the NAND multiplexing structure that copes with the problem of random background charges in single electron tunneling (SET) circuits. Our study shows that, although a rather large amount of redundant components is required, an architecture based on the multiplexing technique could be a faulttolerant system solution for the integration of unreliable nanoelectronic devices affected by dominant transient errors.
In addition, in Chapter 4, a defect and faulttolerant architecture is proposed, that uses the multiplexing technique for its fundamental circuits and a hierarchical reconfigurability in the overall system. It is shown that the required redundancy could be brought back to a moderate level by adding reconfigurability to the system concept. This architecture is robust in an efficient way against both manufacturing defects and transient faults, and tolerates a gate error rate of up to 10 which, for any current microelectronic system, would be unacceptable.
Derived from von Neumann's multiplexing technique, we propose triplicated interwoven redundancy (TIR), as a generalization of triple modular redundancy (TMR), but then with random interconnections. A prototype processor architecture and its simulationbased reliability model have been setup and are used to evaluate the faulttolerance. The processor is, by way of comparison, implemented using both TIR as well as socalled quadded logic. In general, the reliability of a TIR circuit is comparable with that of an equivalent TMR circuit while, for certain interconnect patterns, the TIR structure may present an inferior performance to TMR, due to its interwoven nature in gate interconnections. TIR can be extended to higher orders, which we label Ntuple interwoven redundancy (NIR). The use of 5tuple interwoven redundancy leads to an economical redundancy factor of less than 10 for the reconfigurable system architecture. It has been shown that the design and implementation of restorative devices (voters) are important for TIR/NIR and quadded structures. Only with a simple voter design is it possible to obtain with a higher order of NIR a better system reliability than with TIR. TIR or NIR is in particular suitable for implementation in molecular nanocomputers, which are likely to be fabricated by a manufacturing process of stochastic chemical assembly.
In Chapter 5, superconducting circuits of Josephson junctions have been investigated with as aim to possibly use them in locallyconnected processor structures. Both a classical SIMD computer architecture and an arraybased quantum computer structure are presented that use the same basic circuit, the Josephson junctions. Our ideal is that the classical computer can serve as a pre, post and intermediate processor for the quantum computation that is performed in the heart of the Josephson circuit array. As such, it then establishes a heterogeneous quantum/classical computer for implementations of algorithms such as Shor's factoring algorithm which mixes classical computation steps with quantum computation steps in a single algorithm. Although not specifically worked out and discussed in this study in detail, an architecture in the form of an allreversible computing network based on superconducting circuits of Josephson junctions, could in principle be used for this.
A quantum CNN (cellular nonlinear networks) architecture using the Josephson circuits has also been proposed, presenting a novel computing paradigm for Josephson circuits. Since classical computing architectures (SIMD arrays), quantum computing architectures and semiquantum computing architectures (quantum CNNs) can be simultaneously studied on the same device, the Josephson circuit is a good vehicle for investigating the architectural issues of quantum and nanoelectronic computer systems, independently from the question of which device will be the ultimate implementation vehicle.
This last chapter concludes this dissertation, which can be placed in the "early days" of research on architectures of nanoelectronic and quantum computers.
And beyond this thesis: The scientific papers that form the foundation of the chapters in this thesis have meanwhile been followed up by many new studies in faulttolerant techniques such as using Monte Carlo simulations, bifurcation theory and an exact analysis using combinatorial arguments to investigate the error behavior in a multiplexed nanosystem of Markov chains. Moreover, a probabilisticbased methodology has been proposed for designing nanocomputer architectures based on Markov Random Fields (MRF), and CAD tools are being developed to automate the evaluation of various faulttolerant schemes and their reliability/redundancy tradeoffs. The redundancy techniques, originating from von Neumann, are basically errorcorrecting codes (ECC). The multiplexing construction boils down to the use of a repetition code, in which each symbol of a message is repeated many times to create redundancy. The use of errorcorrecting codes, as well as the issue of faulttolerance in nanocomputing in general, awaits further investigation.
Novel computing systems, envisioned now as adaptive systems based on molecular electronics, biologyinspired selflearning and evolving systems, nonlinear dynamical systems and quantum computers, may in the long term emerge, possibly leading to new types of algorithms and architectures. The choice of algorithms and architectures must aim towards applications in nanotechnology. An architecture will strongly influence the design of devices and circuits, and vice versa: the opportunities and problems found in nanoelectronic devices and circuits will strongly influence the choice of an architecture. In research on nanocomputer architectures, therefore, an interdisciplinary approach must be followed and the success will eventually rely upon a multidisciplinary effort in the fields of chemistry, physics, electrical engineering, computer science, and, perhaps, many others.

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