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arXiv:2012.12589 · Physical Review Applied

Infidelity Induced by Ground-Rydberg Decoherence of the Control Qubit in a Two-Qubit Rydberg-Blockade Gate

Yangyang Liu, Yuan Sun, Zhuo Fu, Peng Xu, Xin Wang, Xiaodong He, Jin Wang, Mingsheng Zhan

Published May 11, 2021• 28 citations
arXivHTMLPDF

Abstract

For neutral-atom qubits, two-qubit gates are typically realized via the Rydberg-blockade effect, which hints at the special status of Rydberg levels compared with regular qubit register states. However, the experimental and theoretical studies that have been done to reveal how the ground-Rydberg coherence of the control-qubit atom affects the fidelity of a two-qubit gate are not yet adequate, especially when all experimental two-qubit gates feature a single atom that stays in the Rydberg state for a certain time. Here, we perform a careful investigation of decoherence in ground-Rydberg transitions in a single atom with various pulse sequences. In particular, based on the commonly used controlled-$Z$ (${C}_{Z}$) gate sequence proposed by D. Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000), we observe that a control-qubit atom subject to a two-qubit entangling process with the $H$-${C}_{Z}$ controlled-not gate scheme experiences a process that is essentially similar to ground-Rydberg Ramsey interference. Then, we build a straightforward theoretical model to link the decoherence time ${\ensuremath{\tau}}_{\mathrm{gr}}$ of the control qubit (extracted from Ramsey fringes of the ground-Rydberg transition) to this ${C}_{Z}$ pulse sequence, and also analyze the typical origins of decoherence effects. Finally, we discuss the loss of fidelity of the ${C}_{Z}$ gate due to the limits imposed by the ground-Rydberg coherence properties, and the prospect of improving fidelity with refined gate protocols.

DOI
10.1103/physrevapplied.15.054020

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For neutral-atom qubits, two-qubit gates are typically realized via the Rydberg-blockade effect, which hints at the special status of Rydberg levels compared with regular qubit register states. However, the experimental and theoretical studies that have been done to reveal how the ground-Rydberg coherence of the control-qubit atom affects the fidelity of a two-qubit gate are not yet adequate, especially when all experimental two-qubit gates feature a single atom that stays in the Rydberg state for a certain time. Here, we perform a careful investigation of decoherence in ground-Rydberg transitions in a single atom with various pulse sequences. In particular, based on the commonly used controlled-ZZZ (CZ{C}_{Z}CZ​) gate sequence proposed by D. Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000), we observe that a control-qubit atom subject to a two-qubit entangling process with the HHH-CZ{C}_{Z}CZ​ controlled-not gate scheme experiences a process that is essentially similar to ground-Rydberg Ramsey interference. Then, we build a straightforward theoretical model to link the decoherence time \ensuremathτgr{\ensuremath{\tau}}_{\mathrm{gr}}\ensuremathτgr​ of the control qubit (extracted from Ramsey fringes of the ground-Rydberg transition) to this CZ{C}_{Z}CZ​ pulse sequence, and also analyze the typical origins of decoherence effects. Finally, we discuss the loss of fidelity of the CZ{C}_{Z}CZ​ gate due to the limits imposed by the ground-Rydberg coherence properties, and the prospect of improving fidelity with refined gate protocols.
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.
Arrays of qubits encoded in the ground-state manifold of neutral atoms trapped in optical (or magnetic) lattices appear to be a promising platform for the realization of a scalable quantum computer. Two-qubit conditional gates between nearest-neighbor qubits in the array can be implemented by exploiting the Rydberg blockade mechanism, as was shown by D. Jaksch et al. [Phys. Rev. Lett. 85, 2208 (2000)]. However, the energy shift due to dipole-dipole interactions causing the blockade falls off rapidly with the interatomic distance, and protocols based on direct Rydberg blockade typically fail to operate between atoms separated by more than one lattice site. In this work, we propose an extension of the protocol of Jaksch et al. for controlled-ZZZ and controlled-not gates which works in the general case where the qubits are not nearest neighbors in the array. Our proposal relies on the Rydberg excitation hopping along a chain of ancilla noncoding atoms connecting the qubits on which the gate is to be applied. The dependence of the gate fidelity on the number of ancilla atoms, the blockade strength, and the decay rates of the Rydberg states is investigated. A comparison between our implementation of a distant controlled-not gate and one based on a sequence of nearest-neighbor two-qubit gates is also provided.
We report results of a ground-state entanglement protocol for a pair of Cs atoms separated by 6 μ m, combining the Rydberg blockade mechanism with a two-photon Raman transition to prepare the Bell state with a loss-corrected fidelity of 0.81(5), equal to the best demonstrated fidelity for atoms trapped in optical tweezers but without the requirement for dynamically adjustable interatomic spacing. Qubit state coherence is also critical for quantum information applications, and we characterise both ground-state and ground-Rydberg dephasing rates using Ramsey spectroscopy. We demonstrate transverse dephasing times ms and s for the qubit levels and achieve long ground-Rydberg coherence times of as required for implementing high-fidelity multi-qubit gate sequences where a control atom remains in the Rydberg state while applying local operations on neighbouring target qubits.
We present experimental results on two-qubit Rydberg-blockade quantum gates and entanglement in a two-dimensional qubit array. Without postselection against atom loss we achieve a Bell state fidelity of $0.73\ifmmode\pm\else\textpm\fi{}0.05$. The experiments are performed in an array of single Cs atom qubits with a site to site spacing of $3.8\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$. Using the standard protocol for a Rydberg-blockade CZ{C}_{Z}CZ​ gate together with single qubit operations we create Bell states and measure their fidelity using parity oscillations. We analyze the role of ac Stark shifts that occur when using two-photon Rydberg excitation and show how to tune experimental conditions for optimal gate fidelity.
Abstract For the quantum error correction and noisy intermediate-scale quantum algorithms to function with high efficiency, the raw fidelity of quantum logic gates on physical qubits needs to satisfy strict requirements. The neutral atom quantum computing equipped with Rydberg blockade gates has made impressive progress recently, which makes it worthwhile to explore its potential in the two-qubit entangling gates, including the controlled-phase gate, and in particular, the CZ gate. Provided the quantum coherence is well preserved, improving the fidelity of Rydberg blockade gates calls for special mechanisms to deal with adverse effects caused by realistic experimental conditions. Here, the heralded very-high-fidelity Rydberg blockade controlled-phase gate is designed to address these issues, which contains self-correction and projection as the key steps. This trailblazing method builds upon the previously established buffer-atom-mediated gate framework, with a special form of symmetry under parity–time transformation playing a crucial role in the process. We further analyze the performance with respect to a few typical sources of imperfections. This procedure can also be regarded as quantum hardware error correction or mitigation. While this paper by itself does not cover every single subtle issue and still contains many oversimplifications, we find it reasonable to anticipate a very-high-fidelity two-qubit quantum logic gate operated in the sense of heralded but probabilistic, whose gate error can be reduced to the level of 10−4–10−6 or even lower with reasonably high possibilities.
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.