Non-Abelian geometric phases in a system of coupled quantum bits

Abstract

A common strategy to measure the Abelian geometric phase for a qubit is to let it evolve along an 'orange slice' shaped path connecting two antipodal points on the Bloch sphere by two different semi- great circles. Since the dynamical phases vanish for such paths, this allows for direct measurement of the geometric phase. Here, we generalize the orange slice setting to the non-Abelian case. The proposed method to measure the non-Abelian geometric phase can be implemented in a cyclic chain of four qubits with controllable interactions.Comment: New title, minor revision, journal ref adde

Rydberg-atom-based scheme of nonadiabatic geometric quantum computation

“…On the other hand, Eqs. (4) and (22) indicate that τ 0 Ω R (t)dt ∼ π. This means that the requirement, τ < τ c and Ω R (t) V, can be indeed satisfied by properly choosing Ω R (t).…”

Fast Holonomic Quantum Computation on Superconducting Circuits With Optimal Control

“…For Δ = 2 × 1 GHz, and the parameter of transmons g k = 2 × 65 MHz, k = 2 × 400 MHz, A = 2 × 370 MHz, 2 = 57 ns,g k,max = 10 MHz by modulatingΩ k (t) with the maximum value to be 2 × 320 MHz. When the initial state is |fgg⟩, a fidelity of 99.44% can be obtained, as plotted in Figure 4, which is done by using the origin Hamiltonian in Equation (14), that is, including all the unwanted higher-order effects induced by the strong microwave driving. In addition, the loss represents the leakage from our computational basis to neighboring states caused directly by the time dependence of the amplitude of the driving pulse, leading to the time dependence of the cross-ac-Stark-shifts terms, which can be compensated by modulating the pulse frequencies k accordingly.…”

Nonadiabatic holonomic gates realized by a single-shot implementation

“…Equations (16) and (17) show that F p and F p decrease with the increasing of the error parameter |ξT | but increase with the increasing of the rotation angle parameter | sin γ|. For a particular gate, while the pulse area error does not affect state |d , it has the most detrimental effect on state |b .…”

“…Although the proposal of nonadiabatic holonomic quantum computation was only recently proposed, it has received increasing attention due to its robustness against control errors and its rapidity without the speed limit of the adiabatic evolution. A number of alternative theoretical and experimental schemes are prompted [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Specially, non-adiabatic holonomic quantum computation has been experimentally demonstrated with a three-level transmon qubit [13], with a NMR quantum information processor [14], and with diamond nitrogen-vacancy centers [19,20], successively.…”