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Quantum Gate and Quantum State Preparation through Neighboring Optimal Control

May 5, 2016 - 3:30am
Yuchen Peng

Successful implementation of a 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 in such a computation. 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. We 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. We illustrate this approach by applying it to all gates in a universal set of quantum gates produced using non-adiabatic rapid passage that has appeared in the literature. Performance improvements are substantial, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall well 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, we further apply the general control theory in a two-step procedure for fault-tolerant logical state preparation, and we 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⟩). We 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.​

Dissertation Committee Chair: Prof. Victor Yakovenko


Dr. Frank Gaitan

Dr. Christopher Lobb

Dr. Frederick Wellstood

Dr. Jacob Taylor

Dr. Christopher Jarzynski

PHY 2202
College Park, MD 20742