Superconducting qubits for quantum annealing applications

Over the last two decades, Quantum Annealing (QA) has grown to be a commercial technology with machines reaching the scale of 5000 interconnected qubits. Two reasons for this progress are the relative ease of implementing adiabatic Hamiltonian control and QA’s partial robustness against errors caused by decoherence. Despite the success of this approach to quantum computation, proving a scaling advantage over classical computation remains an elusive goal to this date. Different strategies are therefore being considered to boost the performance of quantum annealing. These include using more coherent qubit architectures and error-suppression to limit the effect of environmental noise, implementing non-stoquastic driver terms and tailored annealing schedules to enhance the success probability of the algorithm, and using many-body couplers to embed higher-order binary optimisation problems with less resource overhead. This thesis contributes to these efforts in two different ways. The first part provides a detailed numerical analysis and a physical layout for a threebody coupler for flux qubits based on ancillary spins. The application of the coupler in a coherence-signature QA Hamiltonian is also considered and the results of the simulated quantum evolution are compared to the outcomes of classical optimisation on the problem Hamiltonian showing that the classical algorithms cannot correctly reproduce the state distribution at the end of QA. In the second part of the thesis, we develop a numerical method for mapping the Hamiltonian of a composite superconducting circuit to an effective many-qubit Hamiltonian. By overcoming drawbacks of standard reduction methods, this protocol can be used to guide the design of non-stoquastic and many-body Hamiltonian terms, as well as to get a more precise evaluation of the QA schedule parameters, which can greatly improve the outcomes of the optimisation. This numerical work is accompanied by a proposal for an experimental verification of the predictions of the reduction protocol and by some preliminary experimental results

Effective Hamiltonians for interacting superconducting qubits -- local basis reduction and the Schrieffer-Wolff transformation

An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum information. Despite advances in numerical methods to simulate the spectral properties of multi-element superconducting circuits, the literature lacks a consistent and effective method of determining the effective qubit Hamiltonian. Here we address this problem by introducing a novel local basis reduction method. This method does not require any ad hoc assumption on the structure of the Hamiltonian such as its linear response to applied fields. We numerically benchmark the local basis reduction method against other Hamiltonian reduction methods in the literature and report specific examples of superconducting qubits, including the capacitively-shunted flux qubit, where the standard reduction approaches fail. By combining the local basis reduction method with the Schrieffer-Wolff transformation we further extend its applicability to systems of interacting qubits and use it to extract both non-stoquastic two-qubit Hamiltonians and three-local interaction terms in three-qubit Hamiltonians

Research data supporting “Hierarchical Self-Assembly of Cellulose Nanocrystals in a Confined Geometry”

Supporting data for the article titled "Hierarchical Self-Assembly of Cellulose Nanocrystals in a Confined Geometry". The article was accepted for publication in 2016 in the journal "ACS Nano". Electronic supporting Information is available from the publisher (ACS). The data is provided with a description in pdf and a structured set of seven folders compressed in zip, each correlating to a specific data type presented in the published article. The spreadsheet used to plot Figure S12 in the ESI is also included. Folder 1: Phase diagram - containing png of the pictures, as well as a txt, xlsx and pdf of the measurements (Figure S12). Folder 2: Polarised optical microscopy (POM) - containing png pictures with scale-bars Folder 3: Scanning electron microscopy (SEM) - original images in tif (figure S11) Folder 4: Cholesteric pitch determination - data in xlsx and pdf of the Figures 3, S9, S10, S16 Folder 5: Atomic force microscopy (AFM) - svg of the AFM and png of the length distribution analysis (Figure S1) Folder 6: Droplet size determination - data in xlsx and pdf of the droplet size distribution (Figure S17) and evaporation rate (Figure S18) Folder 7: Simulation of cholesteric droplets - png of the simulation with computing parameters in txt (Figure 2), data in xlsx and pdf of optical indices from Bruggeman method (Figure S19), matlab folder with codes in m format.BBSRC [BB/K014617/1], Isaac Newton Trust Cambridge [76933], European Research Council [ERC-2014-STG H2020 639088