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arXiv:1106.0713 · Physical Review A

Cluster-state generation using van der Waals and dipole-dipole interactions in optical lattices

Elena Kuznetsova, T. Bragdon, Robin Côté, Susanne F. Yelin

Published Jan 25, 2012• 26 citations
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Abstract

We present a scalable method for generation of a cluster state for measurement-based quantum computing using van der Waals or dipole-dipole interactions between neutral atoms or polar molecules in an optical lattice. Nearest neighbor entanglement is accomplished by performing a phase gate using interaction of atoms in Rydberg states or molecules in large dipole moment states. All nearest neighbors are sequentially entangled in a finite number of operations, independent of the number of qubits, producing a one-dimensional (1D) cluster state. A universal two-dimensional (2D) cluster state can be generated in several milliseconds in a 2D optical lattice by producing a series of 1D cluster states in one lattice direction, followed by application of the entangling operations in another lattice direction. We discuss the viability of the scheme with Rb Rydberg atoms.

DOI
10.1103/physreva.85.012328

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We present a scalable method for generation of a cluster state for measurement-based quantum computing using van der Waals or dipole-dipole interactions between neutral atoms or polar molecules in an optical lattice. Nearest neighbor entanglement is accomplished by performing a phase gate using interaction of atoms in Rydberg states or molecules in large dipole moment states. All nearest neighbors are sequentially entangled in a finite number of operations, independent of the number of qubits, producing a one-dimensional (1D) cluster state. A universal two-dimensional (2D) cluster state can be generated in several milliseconds in a 2D optical lattice by producing a series of 1D cluster states in one lattice direction, followed by application of the entangling operations in another lattice direction. We discuss the viability of the scheme with Rb Rydberg atoms.
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.
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.
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 study the implementation of quantum random walks (QRWs) in a realistic system, an optical lattice of ultracold Rydberg atoms. The power-law nature of the dipolar interaction between Rydberg atoms influences the behaviour of QRWs. We discuss the QRW with a short-range nearest-neighbour interaction for two types of power-law interactions, the dipole–dipole and the van der Waals interaction. A specific scheme to implement a QRW using Rydberg atoms in different sites of an optical lattice is described, in which the sites are prepared using a blockade mechanism to ensure a single Rydberg atom per site.
We study the possibility to use interaction between a polar molecule in the ground electronic and vibrational state and a Rydberg atom to construct two-qubit gates between molecular qubits and to coherently control molecular states. A polar molecule within the electron orbit in a Rydberg atom can either shift the Rydberg state, or form a Rydberg molecule. Both the atomic shift and the Rydberg molecule states depend on the initial internal state of the polar molecule, resulting in molecular state dependent van der Waals or dipole-dipole interaction between Rydberg atoms. Rydberg atoms mediated interaction between polar molecules can be enhanced up to 10(3) times. We describe how the coupling between a polar molecule and a Rydberg atom can be applied to coherently control molecular states, and specifically, to individually address molecules in an optical lattice, and to non-destructively readout molecular qubits.
We propose a scheme for scalable and universal quantum computation using diatomic bits with conditional dipole-dipole interaction, trapped within an optical lattice. The qubit states are encoded by the scattering state and the bound heteronuclear molecular state of two ultracold atoms per site. The conditional dipole-dipole interaction appears between neighboring bits when they both occupy the molecular state. The realization of a universal set of quantum logic gates, which is composed of single-bit operations and a two-bit controlled-NOT gate, is presented. The readout method is also discussed.