Quantum Gate and Quantum State Preparation through Neighboring Optimal Control
| dc.contributor.advisor | Yakovenko, Victor | en_US |
| dc.contributor.advisor | Gaitan, Frank | en_US |
| dc.contributor.author | Peng, Yuchen | en_US |
| dc.contributor.department | Physics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2016-09-03T05:33:40Z | |
| dc.date.available | 2016-09-03T05:33:40Z | |
| dc.date.issued | 2016 | en_US |
| dc.description.abstract | 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. | en_US |
| dc.identifier | https://doi.org/10.13016/M2KN40 | |
| dc.identifier.uri | http://hdl.handle.net/1903/18539 | |
| dc.language.iso | en | en_US |
| dc.subject.pqcontrolled | Quantum physics | en_US |
| dc.subject.pquncontrolled | high-fidelity | en_US |
| dc.subject.pquncontrolled | logical quantum state | en_US |
| dc.subject.pquncontrolled | neighboring optimal control | en_US |
| dc.subject.pquncontrolled | quantum gate | en_US |
| dc.subject.pquncontrolled | robust | en_US |
| dc.title | Quantum Gate and Quantum State Preparation through Neighboring Optimal Control | en_US |
| dc.type | Dissertation | en_US |
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