Trapped-Ion Quantum Logic with Global Radiation Fields

Trapped ions are a promising tool for building a large-scale quantum computer. However, the number of required radiation fields for the realization of quantum gates in any proposed ion-based architecture scales with the number of ions within the quantum computer, posing a major obstacle when imagining a device with millions of ions. Here, we present a fundamentally different approach for trapped-ion quantum computing where this detrimental scaling vanishes. The method is based on individually controlled voltages applied to each logic gate location to facilitate the actual gate operation analogous to a traditional transistor architecture within a classical computer processor. To demonstrate the key principle of this approach we implement a versatile quantum gate method based on long-wavelength radiation and use this method to generate a maximally entangled state of two quantum engineered clock qubits with fidelity 0.985(12). This quantum gate also constitutes a simple-to-implement tool for quantum metrology, sensing, and simulation.

Figure 1

(a) Schematic of the linear Paul trap (yellow) fitted with four permanent magnets (blue), arranged to create a strong magnetic field gradient along the trap axis. (b) Illustration of the ${{}^{2}S}_{1/2}$ ground-state hyperfine manifold of two ${{}^{171}\mathrm{Yb}}^{+}$ ions, each being driven by two resonant microwave fields near 12.6 GHz with slightly unequal Rabi frequencies denoted by ${\mathrm{\Omega }}_{\mu {\mathrm{w}}_1}$ and ${\mathrm{\Omega }}_{\mu {\mathrm{w}}_2}$ (see the Supplemental Material [32]). The engineered clock qubit is formed of $|\uparrow ⟩=(|+1⟩-|-1⟩)/\sqrt{2}$ and $|\downarrow ⟩=|0^{\prime }⟩$, which can be manipulated using a rf field coupling $|0^{\prime }⟩$ and $|+1⟩$ with Rabi frequency $\sqrt{2}{\mathrm{\Omega }}_0$.

Figure 2

(a) Populations $P(\uparrow \uparrow )$ (blue), $P(\downarrow \downarrow )$ (red), and $P(\uparrow \downarrow )+P(\downarrow \uparrow )$ (black) after preparing the ion spins in the state $|\downarrow \downarrow ⟩$ and applying the Mølmer-Sørensen fields for a variable time $t$. A maximally entangled state is formed at time $t_g=2.7\mathrm{ms}$. Each data point is the average of 500 measurements and the solid lines are the predicted theoretical curves. (b) Parity $\mathrm{\Pi }=P(\uparrow \uparrow )+P(\downarrow \downarrow )-P(\uparrow \downarrow )-P(\downarrow \uparrow )$ after applying the Mølmer-Sørensen interaction for a time $t_g$, followed by a $\pi /2$ pulse on each ion with variable phase $\varphi$. The signal oscillates as $\cos (2\varphi )$, with an amplitude $A$ that indicates the magnitude of the off-diagonal density matrix elements $|{\rho }_{\downarrow \downarrow ,\uparrow \uparrow }|$ [3]. Each data point is the average of 800 measurements and the black line is a fit to the data.

Figure 3

Ions are confined in a two-dimensional $X$-junction surface trap architecture. Local dc electrodes are used to shift the center of the trapping potentials in the magnetic field gradient in order to tune a particular zone in resonance with a particular set of microwave and rf fields (illustrated in the dashed box). The ion displacements in the green (red) zones tune the respective ions into resonance with the global fields to realize single- (two-)qubit gates while no shift is applied to the blue zones, making all globally applied fields off resonant for ions located in these zones. Current-carrying wires (not shown for clarity) located below each gate zone (indicated by yellow lines) create a static magnetic field gradient local within each gate zone.