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arXiv:1611.00750 · Physical Review Applied

Rydberg Quantum Gates Free from Blockade Error

Xiaofeng Shi

Published Jun 12, 2017• 56 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevapplied.7.064017

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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.
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 introduce a novel family of protocols for entangling gates for neutral atom qubits based on the Rydberg blockade mechanism.These protocols realize controlled-phase gates through a series of global laser pulses that are on resonance with the Rydberg excitation frequency.We analyze these protocols with respect to their robustness against calibration errors of the Rabi frequency or shot-to-shot laser intensity fluctuations, and show that they display robustness in various fidelity measures.In addition, we discuss adaptations of these protocols in order to make them robust to atomic-motion-induced Doppler shifts as well.
Abstract Quantum gates and entanglement based on dipole–dipole interactions of neutral Rydberg atoms are relevant to both fundamental physics and quantum information science. The precision and robustness of the Rydberg-mediated entanglement protocols are the key factors limiting their applicability in experiments and near-future industry. There are various methods for generating entangling gates by exploring the Rydberg interactions of neutral atoms, each equipped with its own strengths and weaknesses. The basics and tricks in these protocols are reviewed, with specific attention paid to the achievable fidelity and the robustness to the technical issues and detrimental innate factors.
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.
In any physical platform, two ingredients are essential for quantum information processing: single-qubit control, and entangling interactions between qubits. Neutral atoms can be individually controlled with high fidelity and are resilient to environmental noise, making them attractive candidates for implementing quantum information protocols. However, achieving strong interactions remains a major obstacle. One way to increase the interaction strength between neutral atoms is to excite them into high-lying Rydberg states, which exhibit large electric dipole moments (and by extension, strong electric dipole-dipole interactions). By slowly ramping up the Rydberg level coupling in a system, one can "dress'' the atomic ground states with some Rydberg character; this maps the Rydberg dipole interaction to an effective interaction between ground states. Such Rydberg-dressed interaction is the focus of this dissertation. After describing the physics of the Rydberg-dressed interaction, we propose three protocols that demonstrate its versatility and provide a framework for considering some of the details of realistic implementation. In all three cases, Rydberg dressing --- along with some form of single-atom control --- is used to generate highly entangled states of interest. Our first proposal relates to the adiabatic model of quantum computing, in which solutions to problems are encoded in the ground states of carefully engineered Hamiltonians. The Rydberg-dressed interaction can provide nonlinear Hamiltonian terms, allowing us to encode NP-hard and other interesting problems. We model this protocol in the presence of decoherence, and find that computational fidelities of ~0.98 for four atoms should be possible with currently realistic experimental parameters. Our second proposal is also related to quantum computing, this time in the circuit model. The Rydberg-dressed interaction can be used to generate a controlled-NOT logic gate which, when interwoven with single-qubit gates, can perform universal quantum computation. Experimentally, noise due to atomic thermal motion has been a primary limitation on the fidelities of these gates. We show that a Doppler-free setup, with counterpropagating lasers, effectively suppresses this type of noise, allowing simulated fidelities of up to ~0.998 per gate. Such strong suppression is only possible because the Doppler-free configuration can harness the natural robustness of adiabatic dressing; other gate schemes using, e.g., resonant pulses, do not exhibit the same degree of improvement. Finally, we consider exploiting the many-body character of the Rydberg-dressed interaction to generate collective entanglement in mesoscopic ensembles of neutral atoms. An atomic ensemble uniformly illuminated by a single Rydberg-exciting laser is isomorphic to the well-known Jaynes-Cummings model. In addition to adapting generic Jaynes-Cummings entanglement protocols developed in other platforms, one can apply microwaves to drive entanglement in a way that is unique to the atomic platform. We prove that by allowing the microwave phase to vary in time, one can generate arbitrary symmetric states of the ensemble. While this method compares favorably with other entanglement protocols in many ways, the required frequency of phase switching presents a fundamental limitation on its effectiveness. To mitigate this, we propose a variant scheme in which parameters are chosen to only allow excitations within the system's dressed-ground subspace; this effectively cuts phase switching demands in half. All three protocols serve to illustrate the power of the Rydberg-dressed interaction and suggest directions for future study.
We propose a versatile control protocol based on modulated zero-pulse-area fields that dynamically suppresses Rydberg excitation while retaining Rydberg-Rydberg interactions as an entangling phase resource. This mechanism enables single-step, perfectly entangling phase gates for arbitrary blockade strengths, eliminating finite-blockade errors even when the Rabi frequency approaches or exceeds the interaction energy. The approach defines a new operational regime for Rydberg-blockade quantum logic in which speed, fidelity, and robustness are achieved simultaneously within a simple dynamical framework. Owing to its simplicity and generality, the technique is compatible with a wide range of neutral-atom architectures and offers a promising route toward scalable, high-fidelity quantum computation and simulation.