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Physical Review A

High-quality parallel entangling gates in long mixed-species ion chains

Lin Cheng, Sheng-Chen Liu, Gui-Zhong Yao, Ying-Xiang Wang, Liang-You Peng, Qihuang Gong

Published Oct 9, 2023• 5 citations
Publisher

Abstract

A universal quantum computer is an ultimate pursuit, which should possess the ability to perform entangling gate operations in parallel with high quality in a scalable fashion. However, for a long trapped-ion chain, the simultaneous implementation of two-qubit quantum gates is a challenging task due to the drastic increase of the crosstalk resulting from the collective motional modes. In this paper, by utilizing the structure of the localized motional modes in the long mixed-species ion chain, we propose a highly efficient linear iterative scheme to eliminate the crosstalk within the neighboring pairs. We show that this scheme allows the realization of high-fidelity, low-crosstalk, scalable, parallel two-qubit gates with only a few pulse segments for the long chain. In addition, by considering the practical experimental feasibility, we optimize the laser power and improve the robustness against the random static drifts of the motional frequencies.

DOI
10.1103/physreva.108.042603

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A universal quantum computer is an ultimate pursuit, which should possess the ability to perform entangling gate operations in parallel with high quality in a scalable fashion. However, for a long trapped-ion chain, the simultaneous implementation of two-qubit quantum gates is a challenging task due to the drastic increase of the crosstalk resulting from the collective motional modes. In this paper, by utilizing the structure of the localized motional modes in the long mixed-species ion chain, we propose a highly efficient linear iterative scheme to eliminate the crosstalk within the neighboring pairs. We show that this scheme allows the realization of high-fidelity, low-crosstalk, scalable, parallel two-qubit gates with only a few pulse segments for the long chain. In addition, by considering the practical experimental feasibility, we optimize the laser power and improve the robustness against the random static drifts of the motional frequencies.
Ion trap quantum computers are based on modulating the Coulomb interaction between atomic ion qubits using external forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals by using a small and fixed number of motional modes, simplifying the scaling of ion trap quantum computers. We present analytical work that shows that gate operations need not couple to the motion of distant ions, allowing parallel entangling gates with a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also experimentally demonstrate high-fidelity entangling gates on a fully connected set of seventeen 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ qubits using simple laser pulse shapes that primarily couple to just a few modes.
Almost every quantum circuit is built with two-qubit gates in the current stage, which are crucial to the quantum computing in any platform. The entangling gates based on Mølmer-Sørensen schemes are widely exploited in the trapped-ion system, with the utilization of the collective motional modes of ions and two laser-controlled internal states, which are served as qubits. The key to realize high-fidelity and robust gates is the minimization of the entanglement between the qubits and the motional modes under various sources of errors after the gate operation. In this work, we propose an efficient numerical method to search high-quality solutions for phase-modulated pulses. Instead of directly optimizing a cost function, which contains the fidelity and the robustness of the gates, we convert the problem to the combination of linear algebra and the solution to quadratic equations. Once a solution with the gate fidelity of 1 is found, the laser power can be further reduced while searching on the manifold where the fidelity remains 1. Our method largely overcomes the problem of the convergence and is shown to be effective up to 60 ions, which suffices the need of the gate design in current trapped-ion experiments.
Non-adiabatic two-qubit gate proposals for trapped-ion systems offer superior performance and flexibility over adiabatic schemes at the cost of increased laser control requirements. Existing fast gate schemes are limited by single-qubit transition errors, which constrain the total number of pulses in high-fidelity solutions. We introduce an improved gate search scheme that enables both local and non-local two-qubit gates in chains containing tens of ions. These protocols use a multi-objective machine design approach that incorporates dominant sources of error in the design to ensure the solutions are compatible with existing fast laser controls. We also generalize previous schemes by allowing for unpaired pulses during the gate evolution. By imposing symmetries on the pulse sequences, we eliminate susceptibility to laser phase noise and further simplify the multi-mode control over the state-dependent motion of the ion crystal. We perform a comprehensive analysis of expected gate performance in the presence of random and systematic experimental errors to demonstrate the feasibility of performing microsecond two-qubit gates between arbitrary ion pairs in current linear ion-trap processors of up to 505050 ions with fidelities approaching 99.9%99.9\%99.9%.
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.
High-fidelity and parallel realization in scalable platforms of the two-qubit entangling gates fundamental to universal quantum computing constitutes one of the largest challenges in implementing fault-tolerant quantum computation. Integrated optical addressing of trapped-ion qubits offers routes to scaling the high-fidelity optical control demonstrated to date in small systems. Here we show that in addition to scaling, capabilities practically enabled by integrated optics can substantially alleviate laser powers required for both light-shift (LS) and Molmer-Sorensen (MS) geometric phase gates acting on long-lived ground-state qubit encodings in a broad range of ion species. In the proposed gate schemes utilizing carrier nulling via ion positioning at phase-stable standing-wave (SW) nodes, our calculations suggest that suppressed spontaneous photon scattering at the SW node allows for gate drives operating at smaller Raman detunings, resulting in approximately an order-of-magnitude reduction in power requirement (and significantly larger in certain parameter regimes) for gates of a given duration and scattering-limited fidelity as compared to conventional running wave (RW)-based approaches. The SW schemes have the additional benefit of simultaneously eliminating undesired coherent couplings that typically limit gate speeds. Our work quantifies power requirements for multiple ion species and enhancements to be expected from carrier-nulled configurations practically enabled by integrated delivery, and informs experiments and systems for realization of fast and power-efficient laser-based entangling gates in scalable platforms.
Trapped-ion quantum computers have demonstrated high-performance gate operations in registers of about ten qubits.However, scaling up and parallelizing quantum computations with long one-dimensional (1D) ion strings is an outstanding challenge due to the global nature of the motional modes of the ions, which mediate qubit-qubit couplings.Here, we devise methods to implement scalable and parallel entangling gates by using engineered localized phonon modes.We propose to tailor such localized modes by tuning the local potential of individual ions with programmable optical tweezers.Localized modes of small subsets of qubits form the basis to perform entangling gates on these subsets in parallel.We demonstrate the inherent scalability of this approach by presenting analytical and numerical results for long 1D ion chains and even for infinite chains of uniformly spaced ions.Furthermore, we show that combining our methods with optimal coherent control techniques allows realization of maximally dense universal parallelized quantum circuits.