Universal quantum computation requires precision control of the dynamics of qubits. Frequently accurate quantum control is impeded by systematic drifts and other errors. Compensating composite pulse sequences are a resource efficient technique for quantum error reduction. This work describes compensating sequences for ion-trap quantum computers. We introduce a Lie-algebraic framework which unifies all known fully-compensating sequences and admits a novel geometric interpretation where sequences are treated as vector paths on a dynamical Lie algebra. Using these techniques, we construct new narrowband sequences with improved error correction and reduced time costs. We use these sequences to achieve laser addressing of single trapped 40Ca+ ions, even if neighboring ions experience significant field intensity. We also use broadband sequences to achieve robust control of 171Yb+ ions even with inhomogeneous microwave fields. Further, we generalize compensating sequences to correct certain multi-qubit interactions. We show that multi-qubit gates may be corrected to arbitrary accuracy if there exists either two non-commuting controls with correlated errors or one error-free control. A practical ion-trap quantum computer must be extendible to many trapped ions. One solution is to employ microfabricated surface-electrode traps, which are well-suited for scalable designs and integrated systems. We describe two novel surface-electrode traps, one with on-chip microwave waveguides for hyperfine 171Yb+ qubit manipulations, and a second trap with an integrated high numerical aperture spherical micromirror for enhanced fluorescence collection.

For several decades it has been appreciated that quantum computers hold incredible promise to perform calculations intractable to classical computation. However, this promise has be slow to realize. Dozens of quantum systems are currently being investigated for use in quantum information processing - none of which have yet demonstrated algorithms involving more than a handful of qubits and it remains unclear which, if any, of these systems will ultimately compose a scalable, robust quantum information processing architecture. In this thesis we employ analytical, optimal and algebraic control techniques to evaluate various quantum systems for their potential use in quantum information processing. In doing so, we have additionally identified several novel characterization procedures capable of probing both the coherent and incoherent dynamics of quantum systems. The first part of this thesis discusses work motivated by attempts to utilize donor qubits in silicon as quantum bits. We first propose a measurement of the state of a single donor electron spin using two-dimensional electron gas of a field-effect transistor and electrically detected magnetic resonance. We analyze the potential sensitivity of this measurement and show that it is a quantum nondemolition measurement of an electron-encoded state. We then present the first of two novel qubit characterization procedures. We consider the problem of rapidly characterizing a large number of similarly prepared qubits using techniques from optimal experiment design. All qubits are assumed to evolve according to the same physical processes, though the Hamiltonian parameters may vary from device to device - an inevitability in solid state qubits. We use the Cram\'er-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters, and present a complete analysis of the optimal experimental configuration. Though applied to dipole- and exchange-coupled qubits, this technique is widely applicable to other systems. The second part of the thesis discusses the role that control can play in measuring and mitigating noise in qubit systems. Our first result describes a method for quickly simulating the effects of arbitrary markovian noise on qubit systems through the use of a numerically optimized, multi-state Markovian fluctuator. This ability to rapidly simulate the noisy qubit evolution allows us to compute control sequences capable of maximally decoupling the qubit from the noise source. We then introduce the second characterization procedure of the these, showing that a single measurable and controllable qubit may act as a spectrometer of dephasing noise. We show that the formalism of dynamical decoupling can be used to estimate the short-time correlation function of the noise source, while long time correlations may be estimated by a very simple series of free evolution experiments. This technique is applicable to the wide range of physical implementations which suffer from dephasing noise. The final part of this thesis demonstrates that trapped neutral atoms may be utilized for the robust simulation of complex systems exhibiting a topological phase. We present a method to simulate the toric code Hamiltonian stroboscopically, and demonstrate that our technique preserves the ground state degeneracy . Furthermore, we introduce a dissipative mechanism allowing for thermalization of the system to a finite temperature or direct cooling to the ground state manifold.

Nanomagnetism is a rapidly expanding area of research which appears to be able to provide novel applications. Magnetic molecules are at the very bottom of the possible size of nanomagnets and they provide a unique opportunity to observe the coexistence of classical and quantum properties. The discovery in the early 90's that a cluster comprising twelve manganese ions shows hysteresis of molecular origin, and later proved evidence of quantum effects, opened a new research area which is still flourishing through the collaboration of chemists and physicists. This book is the first attempt to cover in detail the new area of molecular nanomagnetism, for which no other book is available. In fact research and review articles, and book chapters are the only tools available for newcomers and the experts in the field. It is written by the chemists originators and by a theorist who has been one of the protagonists of the development of the field, and is explicitly addressed to an audience of chemists and physicists, aiming to use a language suitable for the two communities.

This work unites the concepts of laser cooling and matter-wave interferometry to develop an interferometric laser cooling technique in an experimental system of cold rubidium atoms. Serving as an introduction to graduate level coherent optical atomic manipulation, the thesis describes the theory of stimulated Raman transitions and atom interferometry, along with the experimental methods for preparing and manipulating cold atoms, before building on these foundations to explore tailored optical pulse sequences and novel atomic cooling techniques. Interferometric cooling, originally proposed by Weitz and Hänsch in 2000, is based upon the coherent broadband laser pulses of Ramsey interferometry and in principle allows laser cooling of atomic and molecular species outside the scope of traditional Doppler laser cooling. On the path toward cooling, composite pulses – quantum error correction methods, developed by chemists to mitigate the effects of in homogeneities in NMR spectroscopy – are investigated with a view to improving the performance of atom interferometers.

Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.