Dynamically Corrected Nonadiabatic Geometric Quantum Logic Gates

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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.