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arXiv:2105.05828 · Physical Review Letters

High-Fidelity Bell-State Preparation with Ca + 40 Optical Qubits

Craig R. Clark, Holly N. Tinkey, Brian C. Sawyer, Adam M. Meier, Jan‐Karl Burkhardt, Christopher M. Seck, Christopher M. Shappert, Nicholas D. Guise, Curtis Volin, Spencer D. Fallek, Harley Hayden, Wade G. Rellergert, Kenton R. Brown

Published Sep 24, 2021• 165 citations
arXivHTMLPDF

Abstract

Entanglement generation in trapped-ion systems has relied thus far on two distinct but related geometric phase gate techniques: Mølmer-Sørensen and light-shift gates. We recently proposed a variant of the light-shift scheme where the qubit levels are separated by an optical frequency [B. C. Sawyer and K. R. Brown, Phys. Rev. A 103, 022427 (2021)PLRAAN2469-992610.1103/PhysRevA.103.022427]. Here we report an experimental demonstration of this entangling gate using a pair of ^{40}Ca^{+} ions in a cryogenic surface-electrode ion trap and a commercial, high-power, 532 nm Nd:YAG laser. Generating a Bell state in 35 μs, we directly measure an infidelity of 6(3)×10^{-4} without subtraction of experimental errors. The 532 nm gate laser wavelength suppresses intrinsic photon scattering error to ∼1×10^{-5}.

DOI
10.1103/physrevlett.127.130505

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Entanglement generation in trapped-ion systems has relied thus far on two distinct but related geometric phase gate techniques: Mølmer-Sørensen and light-shift gates. We recently proposed a variant of the light-shift scheme where the qubit levels are separated by an optical frequency [B. C. Sawyer and K. R. Brown, Phys. Rev. A 103, 022427 (2021)PLRAAN2469-992610.1103/PhysRevA.103.022427]. Here we report an experimental demonstration of this entangling gate using a pair of ^{40}Ca^{+} ions in a cryogenic surface-electrode ion trap and a commercial, high-power, 532 nm Nd:YAG laser. Generating a Bell state in 35 μs, we directly measure an infidelity of 6(3)×10^{-4} without subtraction of experimental errors. The 532 nm gate laser wavelength suppresses intrinsic photon scattering error to ∼1×10^{-5}.
To date, the highest-fidelity quantum logic gates between two qubits have been achieved using the geometric-phase gate in trapped ions, with the two leading variants being the M\o{}lmer-S\o{}rensen gate and the light-shift (LS) gate. Both of these approaches have their respective advantages and challenges. For example, the latter is technically simpler and is natively insensitive to optical phases, but it has not been made to work directly on a clock-state qubit. We present a technique for implementing the LS gate that combines the best features of these two approaches: By using a small ($\ensuremath{\sim}\mathrm{MHz}$) detuning from a narrow (dipole-forbidden) optical transition, we are able to operate an LS gate directly on hyperfine clock states, achieving gate fidelities of 99.74(4)99.74(4)%99.74(4) using modest laser power at visible wavelengths. Current gate infidelities appear to be dominated by technical noise, and theoretical modeling suggests a path toward gate fidelity above 99.9999.99%99.99.
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.
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We propose an optical scheme for generating entanglement between co-trapped identical or dissimilar alkaline-earth atomic ions (40Ca+^{40}\mathrm{Ca}^{+}40Ca+, 88Sr+^{88}\mathrm{Sr}^{+}88Sr+, 138Ba+^{138}\mathrm{Ba}^{+}138Ba+, 226Ra+^{226}\mathrm{Ra}^{+}226Ra+) which exhibits fundamental error rates below ${10}^{\ensuremath{-}4}$ and can be implemented with a broad range of laser wavelengths spanning from ultraviolet to infrared. We also discuss straightforward extensions of this technique to include the two lightest group-2 ions (Be+{\text{Be}}^{+}Be+, Mg+{\text{Mg}}^{+}Mg+) for multispecies entanglement. The key elements of this wavelength-insensitive geometric phase gate are the use of a ground (S1/2{S}_{1/2}S1/2​) and a metastable (D5/2{D}_{5/2}D5/2​) electronic state as the qubit levels within a ${\ensuremath{\sigma}}^{z}{\ensuremath{\sigma}}^{z}$ light-shift entangling gate. We present a detailed analysis of the principles and fundamental error sources for this gate scheme which includes photon scattering and spontaneous emission decoherence, calculating two-qubit-gate error rates and durations at fixed laser beam intensity over a large portion of the optical spectrum (300 nm to $2\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{m}$) for an assortment of ion pairs. We contrast the advantages and disadvantages of this technique against previous trapped-ion entangling gates and discuss its applications to quantum information processing and simulation with like and multispecies ion crystals.
Abstract We demonstrate key multi-qubit quantum-logic primitives in a dual-species trapped-ion system based on 40{}^{40}40 40 Ca +{}^{+}+ + and 88{}^{88}88 88 Sr +{}^{+}+ + ions, using two optical qubits with quantum-logic-control frequencies in the red to near-infrared range. With all ionization, cooling, and control wavelengths in a wavelength band similar for the two species and centered in the visible, and with a favorable mass ratio for sympathetic cooling, this pair is a promising candidate for scalable quantum information processing. Same-species and dual-species two-qubit gates, based on the Mølmer–Sørensen interaction and performed in a cryogenic surface-electrode trap, are characterized via the fidelity of generated entangled states; we achieve fidelities of 98.8(2)% and 97.5(2)% in Ca +{}^{+}+ + –Ca +{}^{+}+ + and Sr +{}^{+}+ + –Sr +{}^{+}+ + gates, respectively. For a similar Ca +{}^{+}+ + –Sr +{}^{+}+ + gate, we achieve a fidelity of 94.3(3)%, and carrying out a Sr +{}^{+}+ + –Sr +{}^{+}+ + gate performed with a Ca +{}^{+}+ + sympathetic cooling ion in a Sr +{}^{+}+ + –Ca +{}^{+}+
We implement a 2-qubit entangling Mølmer-Sørensen interaction by transporting two cotrapped ^{40}Ca^{+} ions through a stationary, bichromatic optical beam within a surface-electrode Paul trap. We describe a procedure for achieving a constant Doppler shift during the transport, which uses fine temporal adjustment of the moving confinement potential. The fixed interaction duration of the ions transported through the laser beam as well as the dynamically changing ac Stark shift require alterations to the calibration procedures used for a stationary gate. We use the interaction to produce Bell states with fidelities commensurate to those of stationary gates performed in the same system. This result establishes the feasibility of actively incorporating ion transport into quantum information entangling operations.