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arXiv:2301.06356 · Physical Review A

Individual addressing of ion qubits with counterpropagating optical frequency combs

Evgeny V. Anikin, L. A. Akopyan, Mikhail Popov, Yelnury Suleimen, Olga Lakhmanskaya, Kirill Lakhmanskiy

Published Aug 3, 2023• 1 citation
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Abstract

We propose a method of individual single-qubit addressing of linear trapped-ion chains utilizing two ultrastable femtosecond frequency combs. For that, we suggest implementing the single-qubit gates with two counterpropagating frequency combs overlapping on the target ion and causing the ac Stark shift between the qubit levels. With analytical calculations and numerical modeling, we show that the arbitrary single-qubit rotations can be indeed realized using only laser fields propagating along the ion chain. We analyze the error sources for the proposed addressing method and prove that it allows implementing the single-qubit gates with high fidelity.

DOI
10.1103/physreva.108.022402

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We propose a method of individual single-qubit addressing of linear trapped-ion chains utilizing two ultrastable femtosecond frequency combs. For that, we suggest implementing the single-qubit gates with two counterpropagating frequency combs overlapping on the target ion and causing the ac Stark shift between the qubit levels. With analytical calculations and numerical modeling, we show that the arbitrary single-qubit rotations can be indeed realized using only laser fields propagating along the ion chain. We analyze the error sources for the proposed addressing method and prove that it allows implementing the single-qubit gates with high fidelity.
We present a scheme utilizing position-dependent ac Stark shifts for doing quantum logic with trapped ions. By a proper choice of direction, position, and size, as well as power and frequency of a far-off-resonant Gaussian laser beam, specific ac Stark shifts can be assigned to the individual ions, making them distinguishable in frequency space. In contrast to previous all-optical based quantum gates with trapped ions, the present scheme enables individual addressing of single ions and selective addressing of any pair of ions for two-ion quantum gates, without using tightly focused laser beams. Furthermore, the decoherence rate due to off-resonant excitations can be made negligible as compared with other sources of decoherence.
We propose a scheme for individual addressing of trapped ion qubits, selecting them via their motional frequency. We show that geometric phase gates can perform single-qubit rotations using the coherent interference of spin-independent and (global) spin-dependent forces. The spin-independent forces, which can be generated via localized electric fields, increase the gate speed while reducing its sensitivity to motional decoherence, which we show analytically and numerically. While the scheme applies to most trapped ion experimental setups, we numerically simulate a specific laser-free implementation, showing cross-talk errors below ${10}^{\ensuremath{-}6}$ for reasonable parameters.
Abstract To date, individual addressing of ion qubits has relied primarily on local Rabi or transition frequency differences between ions created via electromagnetic field spatial gradients or via ion transport operations. Alternatively, it is possible to synthesize arbitrary local one-qubit gates by leveraging local phase differences in a global driving field. Here we report individual addressing of 40Ca+ ions in a two-ion crystal using axial potential modulation in a global gate laser field. We characterize the resulting gate performance via one-qubit randomized benchmarking, applying different random sequences to each co-trapped ion. We identify the primary error sources and compare the results with single-ion experiments to better understand our experimental limitations. These experiments form a foundation for the universal control of two ions, confined in the same potential well, with a single gate laser beam.
Trapped ions boast long coherence times and excellent gate fidelities, making them a useful platform for quantum information processing. Scaling to larger numbers of ion qubits in RF Paul traps demands great effort. Another technique for trapping ions is via a Penning trap where a 2D crystal of hundreds of ions is formed by controlling the rotation of the ions in the presence of a strong magnetic field. However, the rotation of the ion crystal makes single ion addressability a significant challenge. We propose a protocol that takes advantage of a deformable mirror to introduce AC Stark shift patterns that are static in the rotating frame of the crystal. Through numerical simulations we validate the potential of this protocol to perform high-fidelity single-ion gates in crystalline arrays of hundreds of ions.
Large-scale programmable trapped ion hardware, featuring high gate fidelity and long coherence times, is promising for realizing a practical fault-tolerant quantum computer (FTQC). However, individual addressing (IA) methods, which are important for implementing programmable gates in near-term quantum devices, can lead to undesired errors between the target ions and neighboring ions. In this work, we present a low-crosstalk optical addressing system based on multiple optical objectives and acousto-optic deflectors (AODs) with a symmetrical configuration. Two counter-propagating Raman operation beams are both tightly focused, generating an overlapping spot with a waist radius of approximately $1~\upmu\mathrm{m}$, to address the target ion. As a result, IA crosstalk, characterized by Rabi rate crosstalk on the spectator ion, is measured to be 1.19(5)×10−31.19(5)\times10^{-3}1.19(5)×10−3, with the two ions separated by approximately 5.5~$\upmu\mathrm{m}$. This low-crosstalk optical addressing system holds promise for high-fidelity entangling operations, and the symmetrically-configured AODs in our method can be readily extended to two dimensions to address a two-dimensional ion crystal.
Geometric phase gates with addressed laser radiation are widely used in trapped-ion quantum computers to drive high-fidelity entangling gates on an arbitrary qubit pair of a larger ion chain. Such programmable connectivity exploits the collective phonons to mediate the desired interaction, while simultaneously achieving robustness to their thermal fluctuations by a careful calibration of the gate time with respect to the laser and vibrational-mode frequencies. Crosstalk errors can arise when the spectator qubits, which should ideally remain idle during the gate, are partially driven by the laser fields. The minimal crosstalk, which is set by the laser beam size on the spectator ions, can be achieved when the addressing beams propagate perpendicular to the ion chain. However, this results in exciting the radial phonons, and can complicate achieving high-fidelities as the ion chain grows due to the so-called spectral mode crowding. In this work, we present the theoretical description of a scheme recently implemented by Faorlin et al.al.al.. This scheme overcomes these complications by engineering addressable state-dependent forces along the ion-chain with laser beams that propagate perpendicular to it through the use of structured light gradients. In this way, one can excite the axial phonons and avoid the spectral mode crowding, while simultaneously minimizing the crosstalk. We present a detailed derivation of the entangling gate scheme, together with analytical closed-form expressions for the leading contribution to the gate error caused by thermal motional fluctuations and dephasing noise. Our results confirm that such fluctuations account for up to 93%\%% of the error budget under the operating conditions of the gate implemented by Faorlin et al.al.al.. We identify target parameters to reduce the motional error from the reported 10−310^{-3}10−3 to the 10−510^{-5}10−5 level.