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arXiv:2305.03450 · Physical Review Letters

Breaking the Entangling Gate Speed Limit for Trapped-Ion Qubits Using a Phase-Stable Standing Wave

Sebastian Saner, O. Băzăvan, Mariella Minder, P. Drmota, D. J. Webb, G. Araneda, R. Srinivas, D. M. Lucas, Christopher J. Ballance

Published Dec 1, 2023• 25 citations
arXivHTMLPDF

Abstract

All laser-driven entangling operations for trapped-ion qubits have hitherto been performed without control of the optical phase of the light field, which precludes independent tuning of the carrier and motional coupling. By placing $^{88}{\mathrm{Sr}}^{+}$ ions in a $\ensuremath{\lambda}=674\text{ }\text{ }\mathrm{nm}$ standing wave, whose relative position is controlled to $\ensuremath{\approx}\ensuremath{\lambda}/100$, we suppress the carrier coupling by a factor of 18, while coherently enhancing the spin-motion coupling. We experimentally demonstrate that the off-resonant carrier coupling imposes a speed limit for conventional traveling-wave M\o{}lmer-S\o{}rensen gates; we use the standing wave to surpass this limit and achieve a gate duration of $15\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{s}$, restricted by the available laser power.

DOI
10.1103/physrevlett.131.220601

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All laser-driven entangling operations for trapped-ion qubits have hitherto been performed without control of the optical phase of the light field, which precludes independent tuning of the carrier and motional coupling. By placing 88Sr+^{88}{\mathrm{Sr}}^{+}88Sr+ ions in a \ensuremathλ=674  nm\ensuremath{\lambda}=674\text{ }\text{ }\mathrm{nm}\ensuremathλ=674  nm standing wave, whose relative position is controlled to \ensuremath≈\ensuremathλ/100\ensuremath{\approx}\ensuremath{\lambda}/100\ensuremath≈\ensuremathλ/100, we suppress the carrier coupling by a factor of 18, while coherently enhancing the spin-motion coupling. We experimentally demonstrate that the off-resonant carrier coupling imposes a speed limit for conventional traveling-wave M\o{}lmer-S\o{}rensen gates; we use the standing wave to surpass this limit and achieve a gate duration of 15  \ensuremathμs15\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{s}15  \ensuremathμs, restricted by the available laser power.
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.
We propose a scheme to generate a superposition of motional coherent states with arbitrary coefficients on a line in phase space and implement a quantum controlled phase-gate for multiple trapped ions with a single standing-wave laser pulse whose carrier frequency is tuned to the ions transition. In the scheme each ion does not need to be exactly positioned at the node of the standing wave, which is very important from viewpoint of experiment. Furthermore, our scheme may allow the generation of a superposition of coherent states with large mean phonon number for a large number of trapped ions in a fast way by choosing suitable laser intensity. We show that it can also be used to generate maximally entangled states of multiple trapped ions.
Abstract We propose and study ways speeding up of the entangling operations in the trapped ions system with high fidelity. First, we find a scheme to increase the speed of a two-qubit gate without the limitation of trap frequency, which was considered as the fundamental limit. Second, we study the fast gate scheme for entangling more than two qubits simultaneously. We apply the method of applying multiple frequency components on laser beams for the gate operations. In particular, in order to avoid infinite terms from the coupling to carrier transition, we focus on the phase-insensitive gate scheme here. We carefully study the effect of large excitation of motional mode beyond the limit of Lamb–Dicke approximation by including up to second order terms of the Lamb–Dicke parameter. We study the speed limit of multi-qubit global entangling gates without individual addressing requirements. Furthermore, our gates can be made insensitive to the fluctuation of initial motional phases which are difficult to stabilise in the phase-insensitive gate scheme.
A M\o{}lmer-S\o{}rensen entangling gate is realized for pairs of trapped 111Cd+^{111}\mathrm{Cd}^{+}111Cd+ ions using magnetic-field insensitive ``clock'' states and an implementation offering reduced sensitivity to optical phase drifts. The gate is used to generate the complete set of four entangled states, which are reconstructed and evaluated with quantum-state tomography. An average target-state fidelity of 0.79 is achieved, limited by available laser power and technical noise. The tomographic reconstruction of entangled states demonstrates universal quantum control of two ion qubits, which through multiplexing can provide a route to scalable architectures for trapped-ion quantum computing.
The construction of entangling gates with individual addressing capability represents a crucial approach for implementing quantum computation in trapped-ion crystals. Conventional entangling gate schemes typically rely on laser beam wave vectors to couple the ions' spin and motional degrees of freedom. Here, we experimentally demonstrate an alternative method that employs a polarization gradient field generated by a tightly focused laser beam-an approach theoretically proposed as the Magnus effect for quantum logic gate design [Mazzanti et al., Phys. Rev. Res. 5, 033036 (2023)PPRHAI2643-156410.1103/PhysRevResearch.5.033036]. Using this technique, we perform Raman operations on hyperfine qubits encoded in ^{171}Yb^{+} ions, generating spin-dependent forces along axial motional modes in a linear trap. By utilizing an acousto-optic deflector to create arbitrary spot pairs for individual ion addressing in two-ion (four-ion) chains, we achieve Mølmer-Sørensen gates with Bell-state fidelities exceeding 98.7(1)% [and 97.2(4)%]. Further improvements in numerical aperture (NA) and laser power could reduce gate durations while enhancing fidelity by orders of magnitude. This method is compatible with-and can significantly simplify-optical tweezer gate proposals, where motional mode engineering enables scalable trapped-ion quantum computation. The technique can be readily extended to two-dimensional ion crystals, representing a key advancement toward large-scale trapped-ion quantum processors.