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.

Mutual Information-based RBM Neural Networks

(Deep) neural networks are increasingly being used for various computer vision and pattern recognition tasks due to their strong ability to learn highly discriminative features. However, quantitative analysis of their classication ability and design philosophies are still nebulous. In this work, we use information theory to analyze the concatenated restricted Boltzmann machines (RBMs) and propose a mutual information-based RBM neural networks (MI-RBM). We develop a novel pretraining algorithm to maximize the mutual information between RBMs. Extensive experimental results on various classication tasks show the eectiveness of the proposed approach.

ASSESSING QUALITY IN HIGH-UNCERTAINTY MARKETS: ONLINE REVIEWS OF CREDENCE SERVICES

In economics of information theory, credence products are those whose quality is difficult or impossible for consumers to assess, even after they have consumed the product (Darby & Karni, 1973). This dissertation is focused on the content, consumer perception, and power of online reviews for credence services. Economics of information theory has long assumed, without empirical confirmation, that consumers will discount the credibility of claims about credence quality attributes. The same theories predict that because credence services are by definition obscure to the consumer, reviews of credence services are incapable of signaling quality. Our research aims to question these assumptions. In the first essay we examine how the content and structure of online reviews of credence services systematically differ from the content and structure of reviews of experience services and how consumers judge these differences. We have found that online reviews of credence services have either less important or less credible content than reviews of experience services and that consumers do discount the credibility of credence claims. However, while consumers rationally discount the credibility of simple credence claims in a review, more complex argument structure and the inclusion of evidence attenuate this effect. In the second essay we ask, “Can online reviews predict the worst doctors?” We examine the power of online reviews to detect low quality, as measured by state medical board sanctions. We find that online reviews are somewhat predictive of a doctor’s suitability to practice medicine; however, not all the data are useful. Numerical or star ratings provide the strongest quality signal; user-submitted text provides some signal but is subsumed almost completely by ratings. Of the ratings variables in our dataset, we find that punctuality, rather than knowledge, is the strongest predictor of medical board sanctions. These results challenge the definition of credence products, which is a long-standing construct in economics of information theory. Our results also have implications for online review users, review platforms, and for the use of predictive modeling in the context of information systems research.