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arXiv:2008.11736 · Physical Review Research

Rydberg entangling gates in silicon

Eleanor Crane, A. Schuckert, N. H. Le, Andrew J. Fisher

Published Jul 23, 2021• 10 citations
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Abstract

In this paper we propose a Rydberg entangling gate scheme which we demonstrate theoretically to have an order-of-magnitude improvement in fidelities and speed over existing cold atom protocols. It requires a large Rabi frequency compared to the interaction strength, which is difficult in cold atoms, but natural in donors in silicon, where it could help overcome the strenuous requirements on atomic precision donor placement and substantial gate tuning, which so far has hampered scaling. Furthermore, the gate operation would be ultrafast, on the order of picoseconds. We calculate multivalley van der Waals, induced electric dipole and total Rydberg interactions for several donor species using the finite-element method and show that they are important even for low-lying excited states. We show that Rydberg gate operation is possible within the lifetime of donor excited states with 99.9% fidelity for the creation of a Bell state in the presence of decoherence.

DOI
10.1103/physrevresearch.3.033086

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In this paper we propose a Rydberg entangling gate scheme which we demonstrate theoretically to have an order-of-magnitude improvement in fidelities and speed over existing cold atom protocols. It requires a large Rabi frequency compared to the interaction strength, which is difficult in cold atoms, but natural in donors in silicon, where it could help overcome the strenuous requirements on atomic precision donor placement and substantial gate tuning, which so far has hampered scaling. Furthermore, the gate operation would be ultrafast, on the order of picoseconds. We calculate multivalley van der Waals, induced electric dipole and total Rydberg interactions for several donor species using the finite-element method and show that they are important even for low-lying excited states. We show that Rydberg gate operation is possible within the lifetime of donor excited states with 99.9% fidelity for the creation of a Bell state in the presence of decoherence.
Spin qubits of donors in silicon show some of the longest coherence times recorded and hold the promise of scalability with seamless integration of quantum computing into semiconductor fabrication. However, current entangling gate implementations rely on highly challenging precision donor placement and substantial gate tuning, rendering scaling challenging. In this work, we show how to implement placement-insensitive ultrafast entangling gates in deep and shallow donors in silicon by relying on the Rydberg blockade induced by strong interactions between low lying orbital excited states. We calculate multivalley interactions for several donor species using the Finite Element Method, and show that Van der Waals interactions between donors, calculated here for the first time, are important even for low-lying excited states. We show that blockade entangling gate operation is possible within the short lifetime of donor excited states with over 99% fidelity for the creation of a Bell state in the presence of decoherence. This gate substantially relaxes the requirements on single donor placement while allowing for billions of entangling gate operations within the single-qubit lifetime, thus paving the way for large scale quantum computation in silicon.
The advent of digital neutral-atom quantum computers relies on the development of fast and robust protocols for high-fidelity quantum operations. In this work, we introduce a novel scheme for entangling gates using four atomic levels per atom: a ground-state qubit and two Rydberg states. A laser field couples the qubit to one of the two Rydberg states, while a microwave field drives transitions between the two Rydberg states, enabling a resonant dipole-dipole interaction between different atoms. We show that controlled- Z gates can be realized in this scheme without requiring optical phase modulation and relying solely on a microwave field with time-dependent phase and amplitude. We demonstrate that such gates are faster and less sensitive to Rydberg decay than state-of-the-art Rydberg gates based on van der Waals interactions. Moreover, we systematically stabilize our protocol against interatomic distance fluctuations and analyze its performance in realistic setups with rubidium or cesium atoms. Our results open up new avenues to the use of microwave-driven dipolar interactions for quantum computation with neutral atoms.
Ultracold trapped atomic ions excited into highly energetic Rydberg states constitute a promising platform for scalable quantum information processing. Elementary building blocks for such tasks are high-fidelity and sufficiently fast entangling two-qubit gates, which can be achieved via strong dipole-dipole interactions between microwave-dressed Rydberg ions, as recently demonstrated in a breakthrough experiment at https://www.nature.com/articles/s41586-020-2152-9 . We theoretically investigate the performance of three protocols leading to controlled-phase gate operations. Starting from a microscopic description of Rydberg ions in a linear Paul trap, we derive an effective Hamiltonian that faithfully captures the essential dynamics underlying the gate protocols. We then use an optimization scheme to fine-tune experimentally controllable parameters like laser detuning and Rabi frequency to yield maximal gate fidelity under each studied protocol. We show how non-adiabatic transitions resulting from fast laser driving relative to the characteristic time scales of the system detrimentally affect the fidelity. Despite this, we demonstrate that in the realistic scenario of Rydberg ions with finite radiative lifetimes, optimizing the best found gate protocol enables achievement of fidelities as high as 99.25 %99.25\,\%99.25% for a gate time of 0.2 μs0.2\,μ\mathrm{s}0.2μs. This considerably undercuts entangling gate durations between ground-state ions, for which gate times are typically limited by the comparably slower time scales of vibrational modes. Overall, this places trapped Rydberg ions into the regime where fast high-accuracy quantum computing and eventually quantum error correction become possible.
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 $\ensuremath{\mu}\mathrm{m}$.
We analyze a new Rydberg gate design based on the original π−2π−ππ-2π-ππ−2π−π protocol [Jaksch, et. al. Phys. Rev. Lett. {\bf 85}, 2208 (2000)] that is modified to enable high fidelity operation without requiring a strong Rydberg interaction. The gate retains the π−2π−ππ-2π-ππ−2π−π structure with an additional detuning added to the 2π2π2π pulse on the target qubit. The protocol reaches within a factor of 2.39 (1.68) of the fundamental fidelity limit set by Rydberg lifetime for equal (asymmetric) Rabi frequencies on the control and target qubits. We generalize the gate protocol to arbitrary controlled phases. We design optimal target-qubit phase waveforms to generalize the gate across a range of interaction strengths and we find that, within this family of gates, the constant-phase protocol is time-optimal for a fixed laser Rabi frequency and tunable interaction strength. Quantum control techniques are used to design gates that are robust against variations in Rydberg Rabi frequency or interaction strength.
Abstract Ultracold trapped atomic ions excited into highly energetic Rydberg states constitute a promising platform for scalable quantum information processing. Elementary building blocks for such tasks are high-fidelity and sufficiently fast entangling two-qubit gates, which can be achieved via strong dipole–dipole interactions between microwave-dressed Rydberg ions, as recently demonstrated experimentally (Zhang et al 2020 Nature 580 345). We theoretically investigate the performance of three protocols leading to controlled-phase gate operations. Starting from a microscopic description of Rydberg ions in a linear Paul trap, we derive an effective Hamiltonian that faithfully captures the essential dynamics underlying the gate protocols. We then use an optimization scheme to fine-tune experimentally controllable parameters like laser detuning and Rabi frequency to yield maximal gate fidelity under each studied protocol. We show how non-adiabatic transitions resulting from fast laser driving relative to the characteristic time scales of the system detrimentally affect the fidelity. Despite this, we demonstrate that in the realistic scenario of Rydberg ions with finite radiative lifetimes, optimizing the best found gate protocol enables achievement of fidelities as high as 99.25 % for a gate time of 0.2 μ s . This considerably undercuts entangling gate durations between ground state ions, for which gate times are typically limited by the comparably slower time scales of vibrational modes. Overall, this places trapped Rydberg ions into the regime where fast high-accuracy quantum computing and eventually quantum error correction become possible.