Social Influences of Error Monitoring

Adolescence is characterized by dramatic hormonal, physical, and psychological changes, and is a period of risk for affective and anxiety disorders. Pubertal development during adolescence plays a major role in the emergence of these disorders, particularly among girls. Thus, it is critical to identify early biomarkers of risk. One potential biomarker, the error-related negativity (ERN), is an event-related potential following an erroneous response. Individuals with an anxiety disorder demonstrate a greater ERN than healthy comparisons, an association which is stronger in adolescence, suggesting that pubertal development may play a role in the ERN as a predictor of anxiety. One form of anxiety often observed in adolescence, particularly among girls, is social anxiety, which is defined as anxiety elicited by social-evaluative contexts. In adults, enhancements of the ERN in social-evaluative contexts is positively related to social anxiety symptoms, suggesting that the ERN in social contexts may serve as a biomarker for social anxiety. This dissertation examined the ERN in and its relation with puberty and social anxiety among 76 adolescent girls. Adolescent girls completed a flanker task in two different

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.