Dynamically Corrected Nonadiabatic Geometric Quantum Logic Gates

量子计算的前景有可能改变我们信息化经济的格局。然而，量子计算的想法最初被认为是不可能的，因为它依赖于创建量子计算机的指数数量的可能状态的混合，混合的微妙平衡很容易被非常小的错误破坏。量子纠错的概念拯救了量子计算，量子纠错使用大量物理比特对每个逻辑比特进行编码，并在每个计算中插入一系列周期性测量、错误诊断和随后的补救，以实现容错。但是，为了使其工作，物理量子位上的每个操作的保真度必须高于某个阈值，称为特定编码方案的容错阈值。表面代码的容错阈值约为99%，其他代码的容错阈值约为99.99%。虽然一些实验已经显示了超过表面代码阈值的单量子位和双量子位保真度，但总的来说，提高保真度仍然是量子计算成为现实的主要挑战。本研究通过构建对噪声具有鲁棒性的控制协议来解决这一挑战。所采取的方法是结合动力解耦和非绝热几何门控的优点。动态解耦能有效抑制低频噪声，但容易加剧高频噪声。非绝热几何栅极运算能有效抑制高频噪声，但对参数化低频噪声敏感。通过融合这两个概念，本研究寻求在不需要辅助能级的情况下有效抑制宽噪声带宽上的误差。主要研究目标是寻找单量子位非绝热几何门的滤波函数，其特征是在所有频率下对噪声具有鲁棒性，结合单量子位动态解耦技术来改进低频下的滤波函数，为实验实现纳入物理约束，并利用单量子位考虑的见解将新框架扩展到双量子位纠缠操作。获得一组适用于固体实验的鲁棒非绝热几何栅极。成功与否将通过数值模拟计算的平均错误率来评估。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The prospect of quantum computing has the potential to transform the landscape of our information-based economy. However, the idea of quantum computing was initially deemed to be a nonstarter because of its reliance on creating blends of exponentially large numbers of possible states of the quantum computer, blends whose delicate balance could easily be ruined by even very small errors. Quantum computing was rescued by the notion of quantum error correction, which uses a large number of physical bits to encode each logical bit and inserts into each computation a series of periodic measurements, error diagnosis, and subsequent remediation to achieve fault-tolerance. In order for this to work, though, the fidelity of each operation on a physical qubit has to be above a certain threshold, called the fault-tolerance threshold of the particular encoding scheme. The fault-tolerance threshold is around 99% for surface codes, and around 99.99% for other codes. While a few experiments have shown one-qubit and two-qubit fidelities above the surface code threshold, in general raising the fidelity remains a major challenge for quantum computing to become a reality. This research addresses that challenge by constructing control protocols that are robust to noise.The approach taken is to combine the strengths of dynamical decoupling and nonadiabatic geometric gating. Dynamical decoupling is effective in suppressing low-frequency noise, but tends to exacerbate high-frequency noise. Nonadiabatic geometric gate operations are effective in suppressing high-frequency noise, but are sensitive to parametric low-frequency noise. By fusing the two concepts, this research seeks efficient suppression of errors over a broad noise bandwidth without requiring auxiliary energy levels. The major research aims are to find the filter functions of single-qubit nonadiabatic geometric gates that characterize their robustness to noise at all frequencies, to combine with single-qubit dynamical decoupling techniques to improve the filter function at low frequencies, to incorporate physical constraints for experimental implementation, and to use the insight from the single-qubit considerations to extend the new framework to two-qubit entangling operations, attaining a universal set of robust nonadiabatic geometric gates amenable to solid state experiments. Success will be assessed via the average error rates calculated from numerical simulations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.