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

K. A. Landsman, Y. Wu, P. H. Leung, D. Zhu, N. M. Linke, K. R. Brown, L. Duan, and C. Monroe

Phys. Rev. A 100, 022332 – Published 26 August 2019

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

Received 29 May 2019

DOI:https://doi.org/10.1103/PhysRevA.100.022332

Physics Subject Headings (PhySH)

Atom & ion trapping & guiding Coherent control Quantum control Quantum gates Quantum information with trapped ions

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

K. A. Landsman ^1,*, Y. Wu^2,3, P. H. Leung⁴, D. Zhu¹, N. M. Linke¹, K. R. Brown^4,5, L. Duan^3,2, and C. Monroe^1,6

¹Joint Quantum Institute, Department of Physics and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
²Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
³Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China
⁴Department of Physics, Duke University, Durham, North Carolina 27708, USA
⁵Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA
⁶IonQ, Inc., College Park, Maryland 20740, USA

^*kevinlandsman@gmail.com

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Vol. 100, Iss. 2 — August 2019

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Images

Figure 1
(a) Schematic of a long ion chain with two pairs selected to represent a simultaneous entangling gate as described in the main body. Note that the minimal intergate distance between pairs is $n$ , and $p$ is the intragate distance between ion pairs. (b) Log-log plot for crosstalk error ${∥ E ∥}_{⋄}$ vs gate distance $n$ on a 100-ion chain. The gate is designed for a nearest-neighbor pair of ions with $τ = 50 μ s$ , $n_{seg} = 6$ segments, and $μ = 1.016 ω_{1}$ . The green line is fitted from the last five data points. More information can be found in Appendix pp1.
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Figure 2
Partial illustration of the scheme to parallelize gates. $(n + p)$ layers are needed for all possible pairs of ions at an intragate distance of $p$ while maintaining an intergate distance of $n$ between any two pairs. For all possible gates whose distance is less than or equal to $p$ , we need $O [p (n + p)]$ layers in total.
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Figure 3
(a) Frequency and amplitude modulation are plotted for the experimental gate performed on a chain of 17 ions. Phase-space trajectories are closed by changing the frequency modulation, while the amplitude modulation is designed to prevent unwanted Fourier components in the qubit drive. (b) Trajectories of ions through phase space during the gate depicted in (a). Each phonon mode is labeled by its frequency under its respective phase-space plot. The majority of entanglement comes from the geometric phase accumulated when coupling with the two–five highest energy phonons. The rest of the phonons are relatively unexcited and only the highest energy six phonon modes are plotted. The Lamb-Dicke (LD) parameter used for all these plots is based on the common-mode LD parameter.
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Figure 4
Bare gate and parity scan data are plotted for two qubit gates on ions {5,13} and {7,9} in a 17 ion chain. The fidelities are $97 (1) %$ and $95 (1) %$ , respectively. The amplitude was deduced from a least-squares fit and error bars are statistical errors based on a binomial distribution of individual qubit states.
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Figure 5
(a) Optimal gate infidelity vs laser detuning $μ$ for $n = 6$ segments and a total gate time $τ = 50 μ s$ . (b) Rabi frequencies for each segment when $μ$ is chosen at the minimizer of (a). The gate design is optimized through amplitude modulation [20]. There are three curves in each plot: blue for $N = 50$ ions and ion pair 25 and 26, green for $N = 50$ ions and ion pair 10 and 11, and red for $N = 100$ ions and ion pair 50 and 51. All these curves coincide within the resolution of the figure. Here we choose an ion spacing $d = 8 μ m$ , Lamb-Dicke parameter $g_{0} = 0.1$ , transverse trapping frequency $ω_{1} = 2 π \times 3 MHz$ , and 0.5 phonon per mode.
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Figure 6
$| Θ_{i, j} |$ vs $n = | j - i |$ for (a) a gate designed for two ions at a spacing of three separations with $τ = 60 μ s$ , $n_{seg} = 7$ segments, $μ = 1.01403 ω_{1}$ , and (b) a gate designed for two ions at a spacing of five separations with $τ = 100 μ s$ , $n_{seg} = 10$ segments, $μ = 1.01387 ω_{1}$ . The green lines are fitted from the last five data points in each figure.
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