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arXiv:2102.00342 · Physical Review Applied

Transition Slow-Down by Rydberg Interaction of Neutral Atoms and a Fast Controlled-not Quantum Gate

Xiaofeng Shi

Published Nov 23, 2020• 16 citations
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Abstract

Exploring controllable interactions lies at the heart of quantum science. Neutral Rydberg atoms provide a versatile route toward flexible interactions between single quanta. Previous efforts mainly focused on the excitation annihilation (EA) effect of the Rydberg blockade due to its robustness against interaction fluctuation. We study another effect of the Rydberg blockade, namely transition slow-down (TSD). In TSD, a ground-Rydberg cycling in one atom slows down a Rydberg-involved state transition of a nearby atom, which is in contrast to EA that annihilates a presumed state transition. TSD can lead to an accurate controlled-not (cnot) gate with a submicrosecond duration of about $2\ensuremath{\pi}/\mathrm{\ensuremath{\Omega}}+ϵ$ by two pulses, where $ϵ$ is a negligible transient time to implement a phase change in the pulse and $\mathrm{\ensuremath{\Omega}}$ is the Rydberg Rabi frequency. The speedy and accurate TSD-based cnot gate makes neutral atoms comparable (superior) to superconducting (ion-trap) systems.

DOI
10.1103/physrevapplied.14.054058

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Exploring controllable interactions lies at the heart of quantum science. Neutral Rydberg atoms provide a versatile route toward flexible interactions between single quanta. Previous efforts mainly focused on the excitation annihilation (EA) effect of the Rydberg blockade due to its robustness against interaction fluctuation. We study another effect of the Rydberg blockade, namely transition slow-down (TSD). In TSD, a ground-Rydberg cycling in one atom slows down a Rydberg-involved state transition of a nearby atom, which is in contrast to EA that annihilates a presumed state transition. TSD can lead to an accurate controlled-not (cnot) gate with a submicrosecond duration of about 2\ensuremathπ/\ensuremathΩ+ϵ2\ensuremath{\pi}/\mathrm{\ensuremath{\Omega}}+ϵ2\ensuremathπ/\ensuremathΩ+ϵ by two pulses, where ϵϵϵ is a negligible transient time to implement a phase change in the pulse and \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ is the Rydberg Rabi frequency. The speedy and accurate TSD-based cnot gate makes neutral atoms comparable (superior) to superconducting (ion-trap) 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.
We present the first demonstration of a CNOT gate between two individually addressed neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by >8 microm. Using two different gate protocols we measure CNOT fidelities of F=0.73 and 0.72 based on truth table probabilities. The gate was used to generate Bell states with fidelity F=0.48+/-0.06. After correcting for atom loss we obtain an a posteriori entanglement fidelity of F=0.58.
Neutral atoms are promising for large-scale quantum computing, but accurate neutral-atom entanglement depends on large Rydberg interactions which strongly limit the interatomic distances. Via a phase accumulation in detuned Rabi cycles enabled by a Rydberg interaction of similar magnitude to the Rydberg Rabi frequency, we study a controlled-phase gate with an arbitrary phase and extend it to the controlled-not gate. The gates need only three steps for coupling one Rydberg state, depend on an easily accessible van der Waals interaction that naturally arises between distant atoms, and have no rotation error in the weak interaction regime. Importantly, they can work with very weak interactions so that well-separated qubits can be entangled. The gates are sensitive to the irremovable fluctuation of Rydberg interactions, but can still have a fidelity over 98% with realistic position fluctuation of qubits separated over 20 $\ensuremath{\mu}\mathrm{m}$.
Accurate quantum gates are basic elements for building quantum computers. There has been great interest in designing quantum gates by using blockade effect of Rydberg atoms recently. The fidelity and operation speed of these gates, however, are fundamentally limited by the blockade error. Here we propose another type of quantum gates, which are based on Rydberg blockade effect, yet free from any blockade error. In contrast to the `blocking' method in previous schemes, we use Rydberg energy shift to realise a rational generalised Rabi frequency so that a novel π\piπ phase for one input state of the gate emerges. This leads to an accurate Rydberg-blockade based two-qubit quantum gate that can operate in a 0.1μs0.1\mu s0.1μs timescale or faster thanks to that it operates by a Rabi frequency which is comparable to the blockade shift.
We theoretically demonstrate the universal two-qubit CNOT gate between an ionic and an atomic qubit relying on Rydberg excitation of the atom and the resulting phonon blockade in the motional states of the harmonically trapped ion. The phonon blockade arises due to strong ion-atom interaction when the atom is excited to a Rydberg state. For realistic parameters, the gate fidelity is found to be about 90%90\%90%. In a previous paper [S. Mudli {\it et al.} Phys. Rev. A 110, 062618 (2024)], it was shown that a trapped ion can mediate interaction between two largely separated Rydberg atoms, and this mediated interaction can be leveraged to perform a universal two-qubit gate operation between neutral atom qubits in optical tweezers. These demonstrations suggest that an ion-atom hybrid system can serve as a resourceful platform or module for quantum computing and quantum networking as it can utilize the best features of charged as well as neutral atom qubits. Finally, we discuss how to achieve higher gate fidelity by extending our proposed protocol and operating in a different parameter regime.
Rapid, accurate quantum gates are needed for an efficient quantum computer. Among the various physical platforms for logic gates, neutral atoms excited to high-lying states have met with much attention, but have been fundamentally limited by the gate protocol based on the well-known ``blocking'' method. Using a Rydberg interaction to tailor a generalized Rabi oscillation frequency, this study presents a class of exceedingly rapid and accurate two-bit quantum-gate protocols, with implications for quantum control across a wide range of platforms featuring two-body interactions.