Transverse Polarization Gradient Entangling Gates for Trapped-Ion Quantum Computation

TL;DR

Addressing the challenge of scalable, optically addressable entangling gates in trapped-ion quantum computation. The authors demonstrate a polarization-gradient-based approach that uses a tightly focused beam to generate a spin-dependent force, enabling Mølmer-Sørensen gates with axial-mode coupling while suppressing carrier excitations. They report two-qubit gate fidelities exceeding 98.5% on a two-ion chain and 97.2% on a four-ion chain using a 2D AOD for multi-spot addressing, with alignment precision below 100 nm. The method is compatible with optical-tweezer gate proposals and scalable to two-dimensional ion crystals, offering a path toward large-scale trapped-ion processors; future improvements in numerical aperture, laser power, and structured light modes could further increase gate speed and fidelity.

Abstract

The construction of entangling gates with individual addressing capability represents a crucial approach for implementing quantum computation in trapped ion crystals. Conventional entangling gate schemes typically rely on laser beam wave vectors to couple the ions' spin and motional degrees of freedom. Here, we experimentally demonstrate an alternative method that employs a polarization gradient field generated by a tightly focused laser beam, previously proposed as a Magnus-type quantum logic gate. Using this technique, we perform Raman operations on nuclear spin qubits encoded in 171Yb+ ions, generating spin-dependent forces along axial motional modes in a linear trap. By utilizing an acousto-optic deflector to create arbitrary spot pairs for individual ion addressing in two-ion (four-ion) chains, we achieve MS gates with fidelities exceeding 98.5% (97.2%). Further improvements in numerical aperture and laser power could reduce gate durations while enhancing fidelity. This method is compatible with, and can significantly simplify, optical tweezer gate proposals, where motional mode engineering enables scalable trapped-ion quantum computation. The technique can be extended to two-dimensional ion crystals, representing a key step toward large-scale trapped-ion quantum processors.

Figures (8)

• Figure 1: Principle of polarization-gradient-based individual addressing. a, An acousto-optic deflector (AOD) is employed in the addressing system to generate multiple laser spots after the objective lens with high numerical aperture (NA). A multi-tone laser is used to couple to the Raman transition. b, $x$-polarized-focused Gaussian beam creates longitudinal $E_z$ and elliptical polarization near focus. c, For $^{171}\mathrm{Yb}^{+}$, $\Omega(x)\propto\Omega_{+}^2(x)-\Omega_{-}^2(x)$, with $\Omega_{+/-}$ from right/left-circular components. d, Simulated Rabi profile (shaded) for NA=0.4, fit to $\Omega_w(x/w_0)e^{-2x^2/w_0^2}$ (dashed), showing maximal gradient at center. e, Spin-up probability measured by scanning the focus across the ion with $\tau=7\,\mu\mathrm{s}$ pulses, from which the Rabi profile in d is extracted via fitting. f, Multi-qubit gates are implemented using aligned laser spots to address ions, coupling to an axial motional mode g to realize Mølmer-Sørensen gates.
• Figure 2: Mølmer-Sørensen entangling gate in a two-ion chain. a, Population evolution during gate operation, showing maximal entanglement at $t_{\mathrm{gate}}=367\,\mu\mathrm{s}$. Solid lines indicate theoretical predictions. b, Bell state population $P_{00}+P_{11}=0.985(1)$, averaged over 10,200 repetitions. c, Parity oscillation with 0.9887(1) contrast after applying $\pi/2$ pulses with variable phase $\phi$ to each ion. All data represent 400-repetition averages (unless noted), with error bars showing 1 standard error. State preparation and measurement (SPAM) errors are corrected shen2012correcting.
• Figure 3: Gate time and fidelity of MS gate for arbitrary two ions in the four-ion chain. The lower-left corner represents the gate time, while the upper-right corner represents the Bell state fidelity. The population and paritydata are presented in the supplementary materials.
• Figure S1: Laser system for Raman transition and individual addressing. (a) Functional schematic of optical setup. (b) Multi-tone 532 nm laser generation module. The 1064 nm seed laser is modulated by an EOM to generate multiple frequency components. Subsequently, a nonlinear crystal with a bandwidth of approximately 26 GHz converts these components into a 532 nm laser beam containing multiple frequency components.(c) Unequal-arm interferometer module. Since driving Raman transitions requires intensity modulation at 12.64 GHz, we generate an intensity-modulated optical field through an unequal-arm interferometer composed of a pair of AOMs. In the experiment, AOM1 is fixed at 200 MHz, while AOM2 is tuned around a central frequency of 200 MHz to achieve sideband excitation.(d) Individual addressing module. We implement addressing operations using a 2D AOD driven by multiple radio-frequency (RF) signals with distinct frequencies, generating addressable optical spots. After beam expansion, the Raman laser beam is focused onto ions through a 0.4 NA objective. For alignment ease, an achromatic objective is used to image both the ions and 532 nm spots onto a camera simultaneously. (Note: The 369 nm bandpass filter placed before camera is not depicted in the schematic diagram.)
• Figure S2: Excitation spectrum of two-ion chain. The ions are positioned at the center of the light spot. In the experiment, the pulse duration is fixed at 100 µ s, and the detuning of the Raman beam is scanned.