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arXiv:2109.02491 · Physical Review A

High-fidelity entanglement of neutral atoms via a Rydberg-mediated single-modulated-pulse controlled-phase gate

Zhuo Fu, Peng Xu, Yuan Sun, Yangyang Liu, Xiaodong He, Xiao Li, Min Liu, Runbing Li, Jin Wang, Liang Liu, Mingsheng Zhan

Published Apr 21, 2022• 75 citations
arXivHTMLPDF

Abstract

The neutral atom platform has become an attractive choice to study the science of quantum information and quantum simulation, where intense efforts have been devoted to the entangling processes between individual atoms. A two-qubit controlled-phase gate via Rydberg blockade is one of the most essential elements. Recent theoretical studies have suggested the advantages of introducing nontrivial waveform modulation into the gate protocol, which is anticipated to improve its performance towards the next stage. We report our recent experimental results in realizing the two-qubit controlled-phase (${C}_{Z}$) gate via single-modulated-pulse off-resonant modulated driving embedded in a two-photon transition for Rb atoms. It relies on a global driving laser pulse with a carefully calculated smooth waveform to gain the appropriate phase accumulations required by ${C}_{Z}$ gate. Combining this ${C}_{Z}$ gate with global microwave pulses, two-atom entanglement is generated with the raw fidelity of 0.945(6). After accounting for state preparation and measurement errors, we extract the entanglement operation fidelity to be 0.980(7). Our work features completing the ${C}_{Z}$ gate operation within a single pulse to avoid shelved population in the Rydberg levels, thus demonstrating another promising route for realizing a high-fidelity two-qubit gate for the neutral atom platform.

DOI
10.1103/physreva.105.042430

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One can implement fast two-qubit entangling gates by exploiting the Rydberg blockade. Although various theoretical schemes have been proposed, experimenters have not yet been able to demonstrate two-atom gates of high fidelity due to experimental constraints. We propose a novel scheme, which only uses a single Rydberg pulse illuminating both atoms, for the construction of neutral-atom controlled-phase gates. In contrast to the existing schemes, our approach is simpler to implement and requires neither individual addressing of atoms nor adiabatic procedures. With parameters estimated based on actual experimental scenarios, a gate fidelity higher than 0.99 is achievable.

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The neutral atom platform has become an attractive choice to study the science of quantum information and quantum simulation, where intense efforts have been devoted to the entangling processes between individual atoms. A two-qubit controlled-phase gate via Rydberg blockade is one of the most essential elements. Recent theoretical studies have suggested the advantages of introducing nontrivial waveform modulation into the gate protocol, which is anticipated to improve its performance towards the next stage. We report our recent experimental results in realizing the two-qubit controlled-phase (CZ{C}_{Z}CZ​) gate via single-modulated-pulse off-resonant modulated driving embedded in a two-photon transition for Rb atoms. It relies on a global driving laser pulse with a carefully calculated smooth waveform to gain the appropriate phase accumulations required by CZ{C}_{Z}CZ​ gate. Combining this CZ{C}_{Z}CZ​ gate with global microwave pulses, two-atom entanglement is generated with the raw fidelity of 0.945(6). After accounting for state preparation and measurement errors, we extract the entanglement operation fidelity to be 0.980(7). Our work features completing the CZ{C}_{Z}CZ​ gate operation within a single pulse to avoid shelved population in the Rydberg levels, thus demonstrating another promising route for realizing a high-fidelity two-qubit gate for the neutral atom platform.
Neutral-atom arrays serve as an ideal platform to study quantum simulation and quantum logic gates, where intense efforts have been devoted to improving the fidelity of two-qubit gates. We report our recent findings in constructing a different type of two-qubit controlled phase gate protocol with neutral atoms enabled by the Rydberg blockade, which aims at both robustness and high fidelity. It relies upon a modulated driving pulse with a specially tailored smooth waveform to gain appropriate phase accumulations for quantum gates. The major features include finishing a gate operation within a single pulse, not necessarily requiring individual site addressing, not being sensitive to the exact value of the blockade shift, and suppressing the population leakage error and rotation error. Building upon this progress, we further develop an upgrade in the form of dual-pulse off-resonant modulated driving with the major distinct feature of Doppler insensitivity, in order to address the challenge to the fidelity of two-qubit gates caused by residual thermal motion of the cold atoms. In principle, the gate fidelity remains reasonably high over a relatively significant velocity range of the qubit atoms. Moreover, we anticipate that this will inspire future improvements in gate protocols for other types of qubit platforms, and the strategies used here may find applications in the area of quantum optimal control.
Recently, the concept of two-qubit controlled phase gate via off-resonant modulated driving has been introduced into the neutral atom qubit platform, with respect to both single-photon and two-photon ground-Rydberg transitions. In order to reach a better performance practically, further developments are in need to overcome a few known limitations in previous discussions. Here, we thoroughly analyze a variety of modulation styles for two-photon transitions, demonstrating the versatility of off-resonant modulated driving protocols. Furthermore, we show that it is possible to refine the designing process for improved performances for specific finite Rydberg blockade strength values. In particular, a reduced requirement on the blockade strength can be directly linked to an improvement of connectivity in qubit array of neutral atoms. These progress are closely related to the core feature that the atomic wave function acquires a geometric phase from the time evolution, which begins and finishes at the same quantum state. Under reasonable experimental conditions readily available nowadays, we anticipate that the fidelity of such protocols can reach as high as the essential requirement of NISQ even if the effects of technical errors and cold atoms' nonzero temperatures are considered.
We propose an adiabatic protocol for implementing a controlled-phase gate ${\mathrm{CZ}}_{\ensuremath{\theta}}$ with continuous $\ensuremath{\theta}$ of neutral atoms through a symmetrical two-photon excitation process via the second resonance line, 6P6P6P in 87Rb{}^{87}\mathrm{Rb}87Rb, with a single-temporal-modulation-coupling of the ground state and intermediate state. Relying on different adiabatic paths, the phase factor $\ensuremath{\theta}$ of the ${\mathrm{CZ}}_{\ensuremath{\theta}}$ gate can be accumulated on the logic qubit state ∣11⟩|11⟩∣11⟩ alone by calibrating the shape of the temporal pulse where strict zero amplitudes at the start and end of the pulse are not needed. For a wide range of $\ensuremath{\theta}$, we can obtain the fidelity of the ${\mathrm{CZ}}_{\ensuremath{\theta}}$ gate over 99.7% in less than $1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$, in the presence of spontaneous emission from intermediate and Rydberg states. And in particular for $\ensuremath{\theta}=\ensuremath{\pi}$, we benchmark the performance of the CZ gate by taking into account various experimental imperfections, such as Doppler shifts, fluctuation of Rydberg-Rydberg interaction strength, inhomogeneous Rabi frequency, and noise of driving fields, etc., and show that the predicted fidelity is able to maintain at about 98.4% after correcting the measurement error. This gate protocol provides a robustness against the fluctuation of pulse amplitude and a flexible way for adjusting the entangling phase, which may contribute to the experimental implementation of near-term noisy intermediate-scale quantum computation and algorithm with neutral-atom systems.
A neutral-atom system serves as a promising platform for realizing gate-based quantum computing because of its capability to trap and control several atomic qubits in different geometries and the ability to perform strong, long-range interactions between qubits; however, the two-qubit entangling gate fidelity lags behind competing platforms such as superconducting systems and trapped ions. The aim of our work is to design a fast, robust, high-fidelity controlled-ZZZ (cz) gate, based on the Rydberg-blockade mechanism, for neutral atoms. We propose a gate procedure that relies on simultaneous and transitionless quantum driving of a pair of atoms using broadband lasers. By simulating a system of two interacting cesium atoms, including spontaneous emission from excited levels and parameter fluctuations, we yield a Rydberg-blockade cz gate with fidelity 0.9985 over an operation time of $0.12\phantom{\rule{3.33333pt}{0ex}}\mathrm{\textmu{}s}$. Our gate procedure delivers cz gates that are superior than the state-of-the-art experimental cz gate and the simulated cz gates based on adiabatic driving of atoms. Our results show that our gate procedure carries significant potential for achieving scalable quantum computing using neutral atoms.
With the advent of laser cooling and trapping, neutral atoms have become a foundational source of accuracy for applications in metrology and are showing great potential for their use as qubits in quantum information. In metrology, neutral atoms provide the most accurate references for the measurement of time and acceleration. The unsurpassed stability provided by these systems make neutral atoms an attractive avenue to explore applications in quantum information and computing. However, to fully investigate the field of quantum information, we require a method to generate entangling interactions between neutral-atom qubits. Recent progress in the use of highly-excited Rydberg states for strong dipolar interactions has shown great promise for controlled entanglement using the Rydberg blockade phenomenon. I report the use of singly-trapped cesium atoms as qubits for applications in metrology and quantum information. Each atom provides a physical basis for a single qubit by encoding the required information into the ground-state hyperfine structure of cesium. Through the manipulation of these qubits with microwave and optical frequency sources, we demonstrate the capacity for arbitrary single-qubit control by driving qubit rotations in three orthogonal directions on the Bloch sphere. With this control, we develop an atom interferometer that far surpasses the force sensitivity of other approaches by applying the well-established technique of light-pulsed atom-matterwave interferometry to single atoms. Following this, we focus on two-qubit interactions using highly-excited Rydberg states. Through the development of a unique single-photon approach to Rydberg excitation using an ultraviolet laser at 319 nm, we observe the Rydberg blockade interaction between atoms separated by 6.6(3) microns. Motivated by the observation of Rydberg blockade, we study the application of Rydberg-dressed states for a quantum controlled-phase gate. Using a realistic simulation of the dressed-state dynamics, we calculate a controlled-phase gate fidelity of 94% that is primarily limited by Doppler frequency shifts. Finally, we employ our single-photon excitation laser to measure the Rydberg-dressed interaction, thus demonstrating the viability of this approach.
One can implement fast two-qubit entangling gates by exploiting the Rydberg blockade. Although various theoretical schemes have been proposed, experimenters have not yet been able to demonstrate two-atom gates of high fidelity due to experimental constraints. We propose a novel scheme, which only uses a single Rydberg pulse illuminating both atoms, for the construction of neutral-atom controlled-phase gates. In contrast to the existing schemes, our approach is simpler to implement and requires neither individual addressing of atoms nor adiabatic procedures. With parameters estimated based on actual experimental scenarios, a gate fidelity higher than 0.99 is achievable.