Ivanov Peter A, Vitanov Nikolay V
Department of Physics, St. Kliment Ohridski University of Sofia, James Bourchier 5 blvd, 1164, Sofia, Bulgaria.
Sci Rep. 2020 Mar 19;10(1):5030. doi: 10.1038/s41598-020-61766-w.
We propose a method for the realization of the two-qubit quantum Fourier transform (QFT) using a Hamiltonian which possesses the circulant symmetry. Importantly, the eigenvectors of the circulant matrices are the Fourier modes and do not depend on the magnitude of the Hamiltonian elements as long as the circulant symmetry is preserved. The QFT implementation relies on the adiabatic transition from each of the spin product states to the respective quantum Fourier superposition states. We show that in ion traps one can obtain a Hamiltonian with the circulant symmetry by tuning the spin-spin interaction between the trapped ions. We present numerical results which demonstrate that very high fidelity can be obtained with realistic experimental resources. We also describe how the gate can be accelerated by using a "shortcut-to-adiabaticity" field.
我们提出了一种利用具有循环对称性的哈密顿量来实现两比特量子傅里叶变换（QFT）的方法。重要的是，循环矩阵的本征向量是傅里叶模式，并且只要保持循环对称性，就不依赖于哈密顿量元素的大小。QFT的实现依赖于从每个自旋积态到各自量子傅里叶叠加态的绝热跃迁。我们表明，在离子阱中，可以通过调节被俘获离子之间的自旋 - 自旋相互作用来获得具有循环对称性的哈密顿量。我们给出的数值结果表明，利用实际的实验资源可以获得非常高的保真度。我们还描述了如何通过使用“绝热捷径”场来加速门操作。
