用於量子計算的堅固量子邏輯閘

Robust quantum gates for quantum computation

黃嘉賢(Chia-Hsien Huang)

指導教授 ： 管希聖

國立臺灣大學/理學院/物理學研究所/博士(2017年)

https://doi.org/10.6342/NTU201701845

摘要

要實現量子計算(quantum computation)，我們需要一組高保真(high-fidelity)而且堅固(robust)的量子邏輯閘(quantum gate)，來對抗量子位元(qubit)系統中的噪音(noise)並容許系統參數(system parameter)的不準確性(uncertainty)。堅固控制方法(robust control method)可以提供控制脈波(control pulse)來操控並實現高保真而且堅固的量子邏輯閘。可是大部分的堅固控制方法都假設在量子位元系統中的噪音強度並不隨時間而改變，然而這個假設並不總是對的。因此我們提供一套有系統的堅固控制方法，可以有效地處理隨機(stochastic)並且可隨時間改變(time-varying)的噪音。我們的方法可以同時處理多個不同的噪音來源(multiple sources of noise)，可以運用到不同的量子位元系統與不同的噪音模型，並提供連續性(smooth)的控制脈波來操作高保真而且堅固的量子邏輯閘以實現容錯量子計算(fault-tolerant quantum computation)。

接著，我們將此堅固控制方法運用到一個實際的量子位元系統：半導體量子點電子自旋(quantum-dot electron spin)量子位元。最近，澳洲實驗團隊將此量子位元系統建構在純化的同位素矽(isotopically purified silicon)半導體上來改善來自量子位元環境的噪音，並實現二位元(two-qubit)量子邏輯閘。然而，操控二位元量子邏輯閘會伴隨著電的噪音(electrical noise)，而這個噪音使得二位元量子邏輯閘誤差(gate error)無法達到實現容錯量子計算的門檻(threshold)。我們的堅固控制方法可提供最佳化控制脈波(optimal control pulse)，來操控可以抵抗電的噪音之二位元量子邏輯閘，使得邏輯閘誤差遠低於此門檻，並且堅固於來自於系統參數的不準確性。此外我們的最佳化控制脈波也考慮到實驗上對於控制脈波的限制，像是最強脈波強度(maximum pulse strength)限制，還有由波形產生器(waveform generator)的有限頻寬(finite-bandwidth)所造成的濾波效應(filtering effect)。更進一步，我們在同一個控制架構下提供實驗上可實現的最佳化控制脈波，來操控高保真而且堅固的二位元量子邏輯閘與單一位元量子邏輯閘(single-qubit quantum gate)，為實現大尺度(large-scale)容錯量子計算提供重要的一步。

關鍵字

量子計算 ； 最佳化控制 ； 堅固 ； 高保真 ； 隨時變噪音 ； 量子邏輯閘 ； 量子點量子位元

並列摘要

To realize practical quantum computation, a set of high-fidelity universal quantum gates robust against noise and uncertainty in the qubit system is prerequisite. Constructing control pulses to operate quantum gates which meet this requirement is an important and timely issue. In most robust control methods, noise is assumed to be quasi-static, i.e., is time-independent within the gate operation time but can vary between different gates. But this quasi-static-noise assumption is not always valid. Here we develop a systematic method to find pulses for quantum gate operations robust against both low- and high-frequency (comparable to the qubit transition frequency) stochastic time-varying noise. Our approach, taking into account the noise properties of quantum computing systems, can output single smooth pulses in the presence of multisources of noise. Furthermore, our method can be applied to different system models and noise models, and will make essential steps toward constructing high-fidelity and robust quantum gates for fault-tolerant quantum computation (FTQC). We also discuss and compare the gate operation performance by our method with that by the filter-transfer-function method.

Then we apply our robust control method for a realistic system of electron spin qubits in semiconductor (silicon) quantum dots, a promising solid-state system compatible with existing manufacturing technologies for practical quantum computation. A two-qubit controlled-NOT (CNOT) gate, realized by a controlled-phase (C-phase) gate together with some single-qubit gates, has been experimentally implemented recently for quantum-dot electron spin qubits in isotopically purified silicon. But the infidelity of the two-qubit C-phase gate is, primarily due to the electrical control noise, still higher than the required error threshold for FTQC. Here we apply our robust control method to construct high-fidelity CNOT gates with single smooth control pulses robust against the electrical noise and the system parameter uncertainty. The experimental constraints on the maximum pulse strength due to the power limitation of the on-chip electron spin resonance (ESR) line and the filtering effects on the pulses due to the finite bandwidth of waveform generators are also accounted for. The robust and high-fidelity single-qubit gates, together with the two-qubit CNOT gates, can be performed within the same control framework in our scheme, paving the way for large-scale FTQC.

並列關鍵字

quantum computation ； optimal control ； robust ； high-fidelity ； time-varying noise ； quantum gate ； quantum dot qubit

參考文獻

[1] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Phys. Rev. A, vol. 86, p. 032324, Sep 2012.

[2] K. Khodjasteh and L. Viola, “Dynamically error-corrected gates for universal quantum computation,” Phys. Rev. Lett., vol. 102, p. 080501, Feb 2009.

[3] K. Khodjasteh and L. Viola, “Dynamical quantum error correction of unitary operations with bounded controls,” Phys. Rev. A, vol. 80, p. 032314, Sep 2009.

[4] K. Khodjasteh, D. A. Lidar, and L. Viola, “Arbitrarily accurate dynamical control in open quantum systems,” Phys. Rev. Lett., vol. 104, p. 090501, Mar 2010.

[5] K. Khodjasteh, H. Bluhm, and L. Viola, “Automated synthesis of dynamically corrected quantum gates,” Phys. Rev. A, vol. 86, p. 042329, Oct 2012.