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arXiv:1905.10421 · Physical Review A

Two-qubit entangling gates within arbitrarily long chains of trapped ions

K. A. Landsman, Yukai Wu, Pak Hong Leung, Daiwei Zhu, Norbert M. Linke, Kenneth R. Brown, L.-M. Duan, Christopher R. Monroe

Published Aug 26, 2019• 91 citations
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Abstract

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 $^{171}\mathrm{Yb}^{+}$ qubits using simple laser pulse shapes that primarily couple to just a few modes.

DOI
10.1103/physreva.100.022332

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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.
A central challenge in developing practical quantum processors is maintaining low control complexity while scaling to large numbers of qubits. Trapped-ion systems excel in small-scale operations and support rapid qubit scaling via long-chain architectures. However, their performance in larger systems is hindered by spectral crowding in radial motional modes, a problem that forces reliance on intricate pulse-shaping techniques to maintain gate fidelities. Here, we overcome this challenge by developing a trapped-ion processor with an individual-addressing system that generates steerable Hermite-Gaussian beam arrays. The transversal gradient of these beams couples qubits selectively to sparse axial motional modes, enabling to isolate a single or few modes as entanglement mediator. Leveraging this capability, we demonstrate addressable two-qubit entangling gates in chains up to six ions, with Bell-state preparation fidelities consistently around 0.97, achieved without complex pulse shaping. Our method substantially reduces control overhead while preserving scalability, providing a crucial advance toward practical large-scale trapped-ion quantum computing.
A central challenge in developing practical quantum processors is maintaining low control complexity while scaling to large numbers of qubits. Trapped-ion systems excel in small-scale operations and support rapid qubit scaling via long-chain architectures. However, their performance in larger systems is hindered by spectral crowding in radial motional modes, a problem that forces reliance on intricate pulse-shaping techniques to maintain gate fidelities. Here, we overcome this challenge by developing a novel trapped-ion processor with an individual-addressing system that generates steerable Hermite-Gaussian beam arrays. The transverse gradient of these beams couples qubits selectively to sparse axial motional modes, enabling to isolate a single mode as entanglement mediator. Leveraging this capability, we demonstrate addressable two-qubit entangling gates in chains up to six ions with fidelities consistently around 0.97, achieved without complex pulse shaping. Our method significantly reduces control overhead while preserving scalability, providing a crucial advance toward practical large-scale trapped-ion quantum computing.
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.
It is well established that the collective motion of ion crystals can be used as a quantum bus for multiqubit entanglement. However, as the number of ions increases, it becomes difficult to directly entangle ions far apart and resolve all motional modes of the ion crystal. We introduce a scalable and flexible scheme for efficient entanglement between any pair of ions within a large ion chain, using an evenly distributed 50-ion crystal as an example. By performing amplitude and frequency modulation, we find high-fidelity pulse sequences that primarily drive a transverse motional mode with a wavelength of four ion spacings. We present two $500\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$ pulses that can in theory suppress gate errors due to residual motion to below ${10}^{\ensuremath{-}4}$, and observe a trade-off between gate power and robustness against unwanted frequency offsets.
Spectral crowding of collective motional modes limits the fidelity of entangling interactions in trapped-ion quantum processors by inducing off-resonant coupling to spectator modes. We introduce a geometric-phase entangling interaction driven by a transverse, time-dependent structured-light force. By applying the force in a plane orthogonal to the optical propagation direction, we reduce the effects of spectral crowding while preserving single-ion addressing. The scheme is compatible with arbitrary qubit encodings, provided that the qubit states experience a differential AC Stark shift. We experimentally realise high-fidelity two-qubit gates with error rates below 5×10−35\times10^{-3}5×10−3 in ion crystals containing up to 12 ions confined within a single potential well. These results establish gradient-field light-shift gates as a scalable approach to high-fidelity entangling generation in spectrally crowded trapped-ion systems.
Abstract Trapped-ion has shown great advantages in building quantum computers. While high fidelity entangling-gate has been realized for a few ions, how to maintain the high fidelity for large scale trapped-ions remains an open problem. Here, we present an analysis of arbitrary scale ion chains and focus on motional-related errors, reported as one of the leading error sources in state-of-the-art experiments. We theoretically analyze two-qubit entangling-gate infidelity in a large ion crystal under the phase insensitive configuration. To verify our result, we develop an efficient numerical simulation algorithm that avoids exponential increases in of the Hilbert space dimension. For the motional heating error, we derive a much tighter bound of gate infidelity than previously estimated O ( N Γ τ ) , and we give an intuitive understanding from the trajectories in the phase space of motional modes. Our discoveries may inspire the scheme of pulse design against incoherent errors and shed light on the way toward constructing scalable quantum computers with large ion crystals.