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arXiv:1812.03822 · Physical Review Applied

Controlled Phase Gate Protocol for Neutral Atoms via Off-Resonant Modulated Driving

Yuan Sun, Peng Xu, Ping‐Xing Chen, Liang Liu

Published Feb 21, 2020• 41 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevapplied.13.024059

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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.
For neutral atom qubits, the residual thermal motion of the cold atoms constitutes a major challenge that limits the accessible two-qubit gate fidelity. Recently, an interesting type of two-qubit controlled-PHASE quantum gate protocol has been introduced for neutral atom qubit platform, which relies upon off-resonant modulated driving and Rydberg blockade effect. Building upon this progress, we have further developed an upgrade in the form of dual-pulse off-resonant modulated driving. Besides the inherent advantages of avoiding shelving population in Rydberg levels, not necessarily requiring individual site addressing, not sensitive to the exact value of blockade shift while suppressing population leakage error and rotation error, the major new feature of this protocol is Doppler-insensitive. In principle, the gate fidelity remains reasonably high over a relatively significant velocity range of the qubit atoms. Moreover, we anticipate that this protocol will inspire future improvements in quantum gate protocols for other types of qubit platforms, and its strategies may find applications in the area of quantum optimal control.
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.
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.
In the rapid development of cold atom qubit platform, the two-qubit Controlled-PHASE Rydberg blockade gate via off-resonant modulated driving has been making significant progress recently. In pursuit of higher fidelity, faster operation and better robustness, a major upgrade about suppression of high-frequency components in the modulation is called for, and a systematic method has been established here for this purpose. The quintessence of this newly constructed method can be interpreted as filtering out the relatively high frequency ingredients embedded in basis functions to generate the modulation waveforms and then analyzing whether they fulfill the requirement of gate condition. It turns out that appropriate waveforms of two-qubit entangling gate protocols can be successfully established via these frequency-adjusted basis functions, with the help of numerical optimization procedures. Moreover, this timely upgrade version can be further enhanced with adaptions to specific finite Rydberg blockade strength values and dual-pulse technique to overcome residual thermal motion of qubit atoms. Besides theoretical derivations, we also thoroughly investigate the representative modulation patterns, demonstrating the versatility of off-resonant modulated driving method in the design of two-qubit entangling Rydberg blockade gate.
Recently, the method of using a special category of synthetic analytical pulses under off-resonant conditions has improved the experimental performance of two- and multi-qubit gates in the cold atom qubit platform. In order to explore more possibilities and wider ranges of options, we design and analyze the method of almost-resonant modulated driving (ARMD) in constructing fast-speed and high-fidelity quantum logic gates. Whilst the modulation forms the key concept of high-fidelity Rydberg blockade gates so far, the on-off resonance condition can lead to nontrivial nuances in the styles of dynamics, and the ARMD gate protocols have its different characteristic mechanisms in quantum physics compared with the off-resonant gate processes. In particular, ARMD gates usually have abrupt phase changes and at certain points during the time evolution. From a more fundamental point of view, both the resonant and off-resonant methods all together belong to the unitary operation family of fast modulated driving with respect to precisely characterized inter-qubit interactions, which usually allows the quantum logic gate to conclude within one continuous pulse. We anticipate the ARMD gates to work well with the Rydberg dipole-dipole interaction and will serve as a helpful tool in the future studies of the cold atom qubit platform.
Arrays of neutral atoms have emerged as promising platforms for quantum computing. Realization of high-fidelity two-qubit gates with robustness is currently a significant important task for large-scale operations. In this paper, we present a convenient approach for implementing a two-qubit controlled-phase gate using Rydberg blockade. We achieve the noncyclic geometric control with a single modulated pulse. As compared with the control scheme by cyclic evolution that determined by dynamical parameters, the robustness of the proposal against systematic errors will be remarkably improved due to the geometric characteristic. Importantly, the noncyclic geometric control reduces the gate time for small rotation angles and will be more insensitive to the decoherence effect. We accelerate the adiabatic control with the aid of shortcuts to adiabaticity to further shorten the operation time. We apply our protocol to the algorithm of quantum Fourier transformation to show the actual acceleration. Therefore, the proposed scheme will provide an analytical waveforms for arbitrary two-qubit gates and may have important use in the experiments of atomic arrays.