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Plug-and-Play Approach to Non-adiabatic Geometric Quantum Gates
Bao-Jie Liu, Xue-Ke Song, Zheng-Yuan Xue, Xin Wang, Man-Hong Yung
TL;DR
Earlier NHQC gates require restrictive Hamiltonian conditions, and systematic errors can smear geometric phases while limiting compatibility with optimization techniques. NHQC+ relaxes the Hamiltonian constraints to an integral condition, removes the k≠m constraints, and supports compatibility with many pulse-optimization methods. Under Rabi error, NHQC+ was more robust than traditional NHQC and dynamical gates; simulated T- and NOT-gate fidelities reached 99.56% and 99.53%, respectively.
Problem
Earlier NHQC gates require restrictive Hamiltonian conditions, and systematic errors can smear geometric phases while limiting compatibility with optimization techniques.
Source: p. 1Method
NHQC+ relaxes the Hamiltonian constraints to an integral condition, removes the k≠m constraints, and supports compatibility with many pulse-optimization methods.
Source: pp. 1–2Results
Under Rabi error, NHQC+ was more robust than traditional NHQC and dynamical gates; simulated T- and NOT-gate fidelities reached 99.56% and 99.53%, respectively.
Source: p. 4Takeaways & Limitations
The framework supports single-loop geometric gates combined with techniques such as SSSP and KDD, with pulse-optimization performance simulated for nitrogen-vacancy centers.
Source: pp. 1, 5
Abstract
from arXiv · showhide
Nonadiabatic holonomic quantum computation (NHQC) has been developed to shorten the construction times of geometric quantum gates. However, previous NHQC gates require the driving Hamiltonian to satisfy a set of rather restrictive conditions, reducing the robustness of the resulting geometric gates against control errors. Here we show that nonadiabatic geometric gates can be constructed in an extensible way, called NHQC{\th}, for maintaining both flexibility and robustness against certain types of noises. Consequently, this approach makes it possible to incorporate most of the existing optimal control methods, such as dynamical decoupling, composite pulses, and a shortcut to adiabaticity, into the construction of single-looped geometric gates. Furthermore, this extensible approach of geometric quantum computation can be applied to various physical platforms such as superconducting qubits and nitrogen-vacancy centers. Specifically, we performed numerical simulation to show how the noise robustness in recent experimental implementations [Phys. Rev. Lett. 119, 140503 (2017); Nat. Photonics 11, 309 (2017)] can be significantly improved by our NHQC{\th}.approach. These results cover a large class of new techniques combing the noise robustness of both geometric phase and optimal control theory.