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arXiv:1106.0272 · Optics Letters

High-fidelity local addressing of trapped ions and atoms by composite sequences of laser pulses

Svetoslav S. Ivanov, Nikolay V. Vitanov

Published Mar 29, 2011• 55 citations
arXivHTMLPDF

Abstract

A vital requirement for a quantum computer is the ability to locally address, with high fidelity, any of its qubits without affecting their neighbors. We propose an addressing method using composite sequences of laser pulses that dramatically reduces the addressing error in a lattice of closely spaced atoms or ions and at the same time significantly enhances the robustness of qubit manipulations. To this end, we design novel (to our knowledge) high-fidelity composite pulses for the most important single-qubit operations. In principle, this method allows one to beat the diffraction limit, for only atoms situated in a small spatial region around the center of the laser beam are excited, well within the laser beam waist.

DOI
10.1364/ol.36.001275

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A vital requirement for a quantum computer is the ability to locally address, with high fidelity, any of its qubits without affecting their neighbors. We propose an addressing method using composite sequences of laser pulses that dramatically reduces the addressing error in a lattice of closely spaced atoms or ions and at the same time significantly enhances the robustness of qubit manipulations. To this end, we design novel (to our knowledge) high-fidelity composite pulses for the most important single-qubit operations. In principle, this method allows one to beat the diffraction limit, for only atoms situated in a small spatial region around the center of the laser beam are excited, well within the laser beam waist.
We demonstrate a resonance imaging protocol for optical lattices that enables robust preparation and single qubit addressing of atoms with sub-wavelength resolution in 1D. A 3D optical lattice consisting of three sets of independent 1D counter- propagating laser beams provides the trapping potential for the atoms. On this optical lattice platform, a long-period 1D superlattice is imposed by interfering two laser beams at a shallow angle centered at the atoms. This superlattice creates a position-dependent shift of the qubit transition frequency defined between two spin states in the ground manifold. Isolated 2D planes of atoms are prepared by flipping the resonant spins with a microwave pulse and removing the non-resonant spins by pushing them out of the lattice with a resonant laser beam. The periodic planes of atoms that are prepared can be imaged by applying another microwave pulse and detecting the fluorescence from the spins that flip back to the initial state, as a function of superlattice displacement between the preparation and read-out pulses. By employing these new techniques for sub-wavelength imaging, we tested the effectiveness of using composite pulses for addressing the trapped atoms in an optical lattice. Composite pulse techniques can be used to reduce the sensitivity of the addressing to small variations in the relative position and intensity of the lattices. This robustness is achieved by applying numerically generated composite pulses that have a constant atomic response within a target range of relative lattice positions and intensities. We designed a composite microwave pulse that flips the spin with near unit fidelity for all atoms that are positioned within a target spatial region, while conserving the spin of the atoms outside of that region. This cannot be accomplished with plain pulses due to off-resonant excitation. We also expanded the concept of this technique for robustly addressing spins even further to implement independent unitaries, or single qubit quantum gates, across several adjacent lattice sites. Finally, in order to quantitatively measure the fidelity of these robust composite pulses, we perform a randomized benchmarking procedure, which was first proposed by Knill.
Selective laser addressing of a single atom or atomic ion qubit can be improved using narrow-band composite pulse sequences. We describe a Lie-algebraic technique to generalize known narrow-band sequences and introduce sequences related by dilation and rotation of sequence generators. Our method improves known narrow-band sequences by decreasing both the pulse time and the residual error. Finally, we experimentally demonstrate these composite sequences using 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+ ions trapped in a surface-electrode ion trap.
Universal quantum computation requires precision control of the dynamics of qubits. Frequently accurate quantum control is impeded by systematic drifts and other errors. Compensating composite pulse sequences are a resource efficient technique for quantum error reduction. This work describes compensating sequences for ion-trap quantum computers. We introduce a Lie-algebraic framework which unifies all known fully-compensating sequences and admits a novel geometric interpretation where sequences are treated as vector paths on a dynamical Lie algebra. Using these techniques, we construct new narrowband sequences with improved error correction and reduced time costs. We use these sequences to achieve laser addressing of single trapped 40Ca+ ions, even if neighboring ions experience significant field intensity. We also use broadband sequences to achieve robust control of 171Yb+ ions even with inhomogeneous microwave fields. Further, we generalize compensating sequences to correct certain multi-qubit interactions. We show that multi-qubit gates may be corrected to arbitrary accuracy if there exists either two non-commuting controls with correlated errors or one error-free control. A practical ion-trap quantum computer must be extendible to many trapped ions. One solution is to employ microfabricated surface-electrode traps, which are well-suited for scalable designs and integrated systems. We describe two novel surface-electrode traps, one with on-chip microwave waveguides for hyperfine 171Yb+ qubit manipulations, and a second trap with an integrated high numerical aperture spherical micromirror for enhanced fluorescence collection.
Quantum computers based on cold-atom arrays offer long-lived qubits with programmable connectivity, yet their progress toward fault-tolerant operation is limited by the relatively low fidelity of site-selective local control. We introduce an artificial-intelligence (AI) framework that overcomes this limitation. Trained on atom-laser dynamics, a deep neural network autonomously designs composite pulses that improve local control fidelities tenfold while remaining compatible with existing control hardware. We further demonstrate the robustness of these pulses against optical aberrations and beam misalignment. This approach establishes AI-trained pulse compilation for high-fidelity qubit control and can be readily extended to other atom-like platforms, such as trapped ions and solid-state color centers.
We propose a fast and efficient technique to create classes of highly entangled states of trapped ions, such as arbitrary Dicke states and superpositions of them, e.g. NOON states. The ions are initialized in the phonon ground state and are addressed globally with a composite pulse that is resonant with the first motional sideband. The technique is fairly robust to parameter fluctuations and operates on comparatively short time scales, as resonant interactions allow one to use the minimum laser pulse area. The number of single pulses from the composite sequence is equal to the number of ions; thus the implementation complexity grows only linearly with the size of the system. The approach does not require individual addressing of the ions in the trap and can be applied both inside and outside the Lamb–Dicke regime.
We use electronic microwave control methods to implement addressed single-qubit gates with high speed and fidelity, for 43Ca+^{43}{\mathrm{Ca}}^{+}43Ca+ hyperfine ``atomic clock'' qubits in a cryogenic (100 K) surface trap. For a single qubit, we benchmark an error of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ per Clifford gate (implemented using 600 ns $\ensuremath{\pi}/2$ pulses). For 2 qubits in the same trap zone (ion separation $5\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{m}$), we use a spatial microwave field gradient, combined with an efficient four-pulse scheme, to implement independent addressed gates. Parallel randomized benchmarking on both qubits yields an average error $3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ per addressed $\ensuremath{\pi}/2$ gate. The scheme scales theoretically to larger numbers of qubits in a single register.