<p> 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 <i>P<sub>a</sub></i> 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: <i> P<sub>e</sub></i> < <i>P<sub>a</sub>.</i> Estimates of <i> P<sub>a</sub></i> vary widely, though <i>P<sub>a</sub></i> ∼ 10<sup>−4</sup> 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<sup>−4</sup>. </p><p> 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 |β<sub> 01</sub>⟩ = 1/√2(|01⟩ + |10⟩). I show that for ideal (non-ideal) control, an approximate |β<sub>01</sub>⟩ state could be prepared with error probability &epsis; ∼ 10<sup>−6</sup> (10<sup>−5</sup>) with one-shot local operations. Step 2 then takes a block of <i>p</i> pairs of physical qubits, each prepared in |β<sub> 01</sub>⟩ state using Step 1, and fault-tolerantly prepares the logical Bell state for the <i>C</i><sub>4</sub> quantum error detection code.</p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10159056 |
| Date | 30 September 2016 |
| Creators | Peng, Yuchen |
| Publisher | University of Maryland, College Park |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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