Quantum Gate and Quantum State Preparation through Neighboring Optimal Control

Successful implementation of fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold Pa exists for any quantum gate that is to be used for such a computation to be able to continue for an unlimited number of steps. Specifically, the error probability Pe for such a gate must fall below the accuracy threshold: Pe < Pa. Estimates of Pa vary widely, though Pa ∼ 10−4 has emerged as a challenging target for hardware designers. I present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. I illustrate this approach by applying it to a universal set of quantum gates produced using non-adiabatic rapid passage. Performance improvements are substantial comparing to the original (unimproved) gates, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall by 1 to 4 orders of magnitude below the target threshold of 10−4. After applying the neighboring optimal control theory to improve the performance of quantum gates in a universal set, I further apply the general control theory in a two-step procedure for fault-tolerant logical state preparation, and I illustrate this procedure by preparing a logical Bell state fault-tolerantly. The two-step preparation procedure is as follow: Step 1 provides a one-shot procedure using neighboring optimal control theory to prepare a physical qubit state which is a high-fidelity approximation to the Bell state |β01⟩ = 1/√2(|01⟩ + |10⟩). I show that for ideal (non-ideal) control, an approximate |β01⟩ state could be prepared with error probability ϵ ∼ 10−6 (10−5) with one-shot local operations. Step 2 then takes a block of p pairs of physical qubits, each prepared in |β01⟩ state using Step 1, and fault-tolerantly prepares the logical Bell state for the C4 quantum error detection code.

Engineering a Quantum Many-body Hamiltonian with Trapped Ions

While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.

The role of new information and communication technologies (ICTs) in information and communication in science. A conceptual framework and empirical study

Problem This dissertation presents a literature-based framework for communication in science (with the elements partners, purposes, message, and channel), which it then applies in and amends through an empirical study of how geoscientists use two social computing technologies (SCTs), blogging and Twitter (both general use and tweeting from conferences). How are these technologies used and what value do scientists derive from them? Method The empirical part used a two-pronged qualitative study, using (1) purposive samples of ~400 blog posts and ~1000 tweets and (2) a purposive sample of 8 geoscientist interviews. Blog posts, tweets, and interviews were coded using the framework, adding new codes as needed. The results were aggregated into 8 geoscientist case studies, and general patterns were derived through cross-case analysis. Results A detailed picture of how geoscientists use blogs and twitter emerged, including a number of new functions not served by traditional channels. Some highlights: Geoscientists use SCTs for communication among themselves as well as with the public. Blogs serve persuasion and personal knowledge management; Twitter often amplifies the signal of traditional communications such as journal articles. Blogs include tutorials for peers, reviews of basic science concepts, and book reviews. Twitter includes links to readings, requests for assistance, and discussions of politics and religion. Twitter at conferences provides live coverage of sessions. Conclusions Both blogs and Twitter are routine parts of scientists' communication toolbox, blogs for in-depth, well-prepared essays, Twitter for faster and broader interactions. Both have important roles in supporting community building, mentoring, and learning and teaching. The Framework of Communication in Science was a useful tool in studying these two SCTs in this domain. The results should encourage science administrators to facilitate SCT use of scientists in their organization and information providers to search SCT documents as an important source of information.

EXCITON ENGINEERING THROUGH TUNALBLE FLUORESCENT QUANTUM DEFECTS

This thesis demonstrates exciton engineering in semiconducting single-walled carbon nanotubes through tunable fluorescent quantum defects. By introducing different functional moieties on the sp2 lattice of carbon nanotubes, the nanotube photoluminescence is systematically tuned over 68 meV in the second near-infrared window. This new class of quantum emitters is enabled by a new chemistry that allows covalent attachment of alkyl/aryl functional groups from their iodide precursors in aqueous solution. Using aminoaryl quantum defects, we show that the pH and temperature of complex fluids can be optically measured through defect photoluminescence that encodes the local environment information. Furthermore, defect-bound trions, which are electron-hole-electron tri-carrier quasi-particles, are observed in alkylated single-walled carbon nanotubes at room temperature with surprisingly high photoluminescence brightness. Collectively, the emission from defect-bound excitons and trions in (6,5)-single walled carbon nanotubes is 18-fold brighter than that of the native exciton. These findings pave the way to chemical tailoring of the electronic and optical properties of carbon nanostructures with fluorescent quantum defects and may find applications in optoelectronics and bioimaging.