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.

INTEGRATED THRESHOLD-ACTIVATED FEEDBACK MICROSYSTEM FOR REAL-TIME CHARACTERIZATION, SENSING AND TREATMENT OF BACTERIAL BIOFILMS

Biofilms are the primary cause of clinical bacterial infections and are impervious to typical amounts of antibiotics, necessitating very high doses for treatment. Therefore, it is highly desirable to develop new alternate methods of treatment that can complement or replace existing approaches using significantly lower doses of antibiotics. Current standards for studying biofilms are based on end-point studies that are invasive and destroy the biofilm during characterization. This dissertation presents the development of a novel real-time sensing and treatment technology to aid in the non-invasive characterization, monitoring and treatment of bacterial biofilms. The technology is demonstrated through the use of a high-throughput bifurcation based microfluidic reactor that enables simulation of flow conditions similar to indwelling medical devices. The integrated microsystem developed in this work incorporates the advantages of previous in vitro platforms while attempting to overcome some of their limitations. Biofilm formation is extremely sensitive to various growth parameters that cause large variability in biofilms between repeated experiments. In this work we investigate the use of microfluidic bifurcations for the reduction in biofilm growth variance. The microfluidic flow cell designed here spatially sections a single biofilm into multiple channels using microfluidic flow bifurcation. Biofilms grown in the bifurcated device were evaluated and verified for reduced biofilm growth variance using standard techniques like confocal microscopy. This uniformity in biofilm growth allows for reliable comparison and evaluation of new treatments with integrated controls on a single device. Biofilm partitioning was demonstrated using the bifurcation device by exposing three of the four channels to various treatments. We studied a novel bacterial biofilm treatment independent of traditional antibiotics using only small molecule inhibitors of bacterial quorum sensing (analogs) in combination with low electric fields. Studies using the bifurcation-based microfluidic flow cell integrated with real-time transduction methods and macro-scale end-point testing of the combination treatment showed a significant decrease in biomass compared to the untreated controls and well-known treatments such as antibiotics. To understand the possible mechanism of action of electric field-based treatments, fundamental treatment efficacy studies focusing on the effect of the energy of the applied electrical signal were performed. It was shown that the total energy and not the type of the applied electrical signal affects the effectiveness of the treatment. The linear dependence of the treatment efficacy on the applied electrical energy was also demonstrated. The integrated bifurcation-based microfluidic platform is the first microsystem that enables biofilm growth with reduced variance, as well as continuous real-time threshold-activated feedback monitoring and treatment using low electric fields. The sensors detect biofilm growth by monitoring the change in impedance across the interdigitated electrodes. Using the measured impedance change and user inputs provided through a convenient and simple graphical interface, a custom-built MATLAB control module intelligently switches the system into and out of treatment mode. Using this self-governing microsystem, in situ biofilm treatment based on the principles of the bioelectric effect was demonstrated by exposing two of the channels of the integrated bifurcation device to low doses of antibiotics.