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We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum nondemolition type. Two successive readouts are used to analyze the evolution of the qubit and the detector during the measurement. We introduce a simple transition rate model for characterizing the qubit relaxation and the detector switching process. Corrected for qubit relaxation the readout fidelity is at least 95%. Qubit relaxation strongly depends on the driving strength and the state of the oscillator.

We present a method to determine the decay of multiparticle quantum correlations as quantified by the geometric measure of entanglement under the influence of decoherence. With this, we compare the robustness of entanglement in Greenberger-Horne-Zeilinger (GHZ), cluster, W, and Dicke states of four qubits and show that the Dicke state is the most robust. Finally, we determine the geometric measure analytically for decaying GHZ and cluster states of an arbitrary number of qubits.

We present experimental results on the crosstalk between two ac-operated dispersive bifurcation detectors, implemented in a circuit for high-fidelity readout of two strongly coupled flux qubits. Both phase-dependent and phase-independent contributions to the crosstalk are analyzed. For proper tuning of the phase the measured crosstalk is 0.1% and the correlation between the measurement outcomes is less than 0.05%. These results show that bifurcative readout provides a reliable and generic approach for multipartite correlation experiments.

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 address continuous weak linear quantum measurement and argue that it is best understood in terms of statistics of the outcomes of the linear detectors measuring a quantum system, for example, a qubit. We mostly concentrate on a setup consisting of a qubit and three independent detectors that simultaneously monitor three noncommuting operator variables, those corresponding to three pseudospin components of the qubit. We address the joint probability distribution of the detector outcomes and the qubit variables. When analyzing the distribution in the limit of big values of the outcomes, we reveal a high degree of correspondence between the three outcomes and three components of the qubit pseudospin after the measurement. This enables a highfidelity monitoring of all three components. We discuss the relation between the monitoring described and the algorithms of quantum information theory that use the results of the partial measurement. We develop a proper formalism to evaluate the statistics of continuous weak linear measurement. The formalism is based on Feynman-Vernon approach, roots in the theory of full counting statistics, and boils down to a Bloch-Redfield equation augmented with counting fields.

Besides an electric charge, electrons also have a tiny magnetic moment, called spin. In a magnetic field, the spin has two possible orientations: 'spin-up' (parallel to the field) and 'spin-down' (anti-parallel to the field) and can therefore be used as a quantum bit, the computational unit of a quantum computer. For quantum computations, quantum bits must have long relaxation and coherence times. Furthermore, one needs to be able to manipulate and read out the quantum bits. The research in this thesis aims at developing a solid-state quantum bit using electron spins, confined in quantum dots. We perform single-shot read-out of electron spin states and observe long relaxation times. These measurements also reveal that lattice vibrations (phonons) play a dominant role in the spin relaxation process. To increase the spin read-out fidelity we introduce a novel approach to ultrafast charge detection: a high electron mobility transistor operated as a cryogenic pre-amplification stage. Another essential requirement is the ability to coherently manipulate the electron spin, which we achieve by generating an oscillating magnetic field close to the dot. We also use this electron spin resonance technique to indirectly control the surrounding nuclear spins. This electron-nuclear interaction might be used to prepare a nuclear spin environment where fluctuations are reduced.

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 parametric-coupling 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 two-qubit system arise when dealing with multiqubit systems.

The progress in CMOS technology has entered the sub-micron 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 fault-tolerant and locally-coupled 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 fault-tolerant 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 multi-stage 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 fault-tolerant system solution for the integration of unreliable nanoelectronic devices affected by dominant transient errors. In addition, in Chapter 4, a defect- and fault-tolerant 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 simulation-based reliability model have been set-up and are used to evaluate the fault-tolerance. The processor is, by way of comparison, implemented using both TIR as well as so-called 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 N-tuple interwoven redundancy (NIR). The use of 5-tuple 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 locally-connected processor structures. Both a classical SIMD computer architecture and an array-based 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 all-reversible 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 semi-quantum 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 fault-tolerant 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 probabilistic-based 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 fault-tolerant schemes and their reliability/redundancy trade-offs. The redundancy techniques, originating from von Neumann, are basically error-correcting 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 error-correcting codes, as well as the issue of fault-tolerance in nanocomputing in general, awaits further investigation. Novel computing systems, envisioned now as adaptive systems based on molecular electronics, biology-inspired self-learning 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.

The authors have studied low-frequency resistance fluctuations in shadow-evaporated Al/AlOx/Al tunnel junctions. Between 300 and 5 K the spectral density follows a 1/f law. Below 5 K, individual defects distort the 1/f shape of the spectrum. The spectral density decreases linearly with temperature between 150 and 1 K and saturates below 0.8 K. At 4.2 K, it is about two orders of magnitude lower than expected from a recent survey [D. J. Van Harlingen et al., Phys. Rev. B 70, 064510 (2004)]. Due to saturation below 0.8 K the estimated qubit dephasing times at 100 mK are only about two times longer than calculated by Van Harlingen et al.

In this letter, we describe the observation of the interference of conduction paths induced by two donors in a nanoscale silicon transistor, resulting in a Fano resonance. This demonstrates the coherent exchange of electrons between two donors. In addition, the phase difference between the two conduction paths can be tuned by means of a magnetic field, in full analogy to the Aharonov–Bohm effect. One of the crucial ingredients for donor based quantum computation is phase coherent manipulation of electrons. This has not been achieved as yet, and this work presents a stepping stone.

We report both photon- and phonon-assisted tunneling transitions in a linear array of three quantum dots, which can only be understood by considering the full three-dimensionality of the charge stability diagram. Such tunneling transitions potentially contribute to leakage of qubits defined in this system. A detailed understanding of these transitions is important as they become more abundant and complex to analyze as quantum dot arrays are scaled up.