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arXiv:1402.2141 · Physical Review A

One- and two-qubit quantum gates using superimposed optical-lattice potentials

Nils B. Jørgensen, Mark G. Bason, Jacob Friis Sherson

Published Mar 6, 2014• 8 citations
arXivHTMLPDF

Abstract

Steps towards implementing a collision-based two-qubit gate in optical lattices have previously been realized by the parallel merging of all pairs of atoms in a periodicity two superlattice. In contrast, we propose an architecture which allows for the merger of a selected qubit pair in a long-periodicity superlattice structure consisting of two optical lattices with close-lying periodicity. We numerically optimize the gate time and fidelity, including the effects on neighboring atoms and in the presence of experimental sources of error. Furthermore, the superlattice architecture induces a differential hyperfine shift, allowing for single-qubit gates. The fastest possible single-qubit gate times, given a maximal tolerable rotation error on the remaining atoms at various values of the lattice wavelengths, are identified. We find that robust single- and two-qubit gates with gate times of a few hundred microseconds and with error probabilities $\ensuremath{\sim}$${10}^{\ensuremath{-}3}$ are possible.

DOI
10.1103/physreva.89.032306

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Steps towards implementing a collision-based two-qubit gate in optical lattices have previously been realized by the parallel merging of all pairs of atoms in a periodicity two superlattice. In contrast, we propose an architecture which allows for the merger of a selected qubit pair in a long-periodicity superlattice structure consisting of two optical lattices with close-lying periodicity. We numerically optimize the gate time and fidelity, including the effects on neighboring atoms and in the presence of experimental sources of error. Furthermore, the superlattice architecture induces a differential hyperfine shift, allowing for single-qubit gates. The fastest possible single-qubit gate times, given a maximal tolerable rotation error on the remaining atoms at various values of the lattice wavelengths, are identified. We find that robust single- and two-qubit gates with gate times of a few hundred microseconds and with error probabilities \ensuremath{\sim}$${10}^{\ensuremath{-}3} are possible.
We present a complete architecture for scalable quantum computation with ultracold atoms in optical lattices using optical tweezers focused to the size of a lattice spacing. We discuss three different two-qubit gates based on local collisional interactions. The gates between arbitrary qubits require the transport of atoms to neighboring sites. We numerically optimize the nonadiabatic transport of the atoms through the lattice and the intensity ramps of the optical tweezer in order to maximize the gate fidelities. We find overall gate times of a few $100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}$s, while keeping the error probability due to vibrational excitations and spontaneous scattering below ${10}^{\ensuremath{-}3}$. The requirements on the positioning error and intensity noise of the optical tweezer and the magnetic field stability are analyzed and we show that atoms in optical lattices could meet the requirements for fault-tolerant scalable quantum computing.
We make a detailed analysis of error mechanisms, gate fidelity, and scalability of proposals for quantum computation with neutral atoms in addressable (large lattice constant) optical lattices. We have identified possible limits to the size of quantum computations, arising in three-dimensional (3D) optical lattices from current limitations on the ability to perform single-qubit gates in parallel and in 2D lattices from constraints on laser power. Our results suggest that 3D arrays as large as $100\ifmmode\times\else\texttimes\fi{}100\ifmmode\times\else\texttimes\fi{}100$ sites (i.e., $\ensuremath{\sim}{10}^{6}$ qubits) may be achievable, provided two-qubit gates can be performed with sufficiently high precision and degree of parallelizability. The parallelizability of long-range interaction-based two-qubit gates is qualitatively compared to that of collisional gates. Different methods of performing single-qubit gates are compared, and a lower bound of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ is determined on the error rate for the error mechanisms affecting 133Cs^{133}\text{C}\text{s}133Cs in a blue-detuned lattice with Raman-transition-based single-qubit gates, given reasonable limits on experimental parameters.
Fast collisional SWAP\sqrt{\mathrm{SWAP}}SWAP​ gate for fermionic atoms in an optical superlattice
Collisional gates in optical superlattices have recently achieved record fidelities, but their operation times are typically limited by tunneling. Here we propose and analyze an alternative route to a fast SWAP\sqrt{\mathrm{SWAP}}SWAP​ gate for two fermionic atoms in an optical superlattice based on optimized, time-dependent control of the short and long lattice depths. The gate is implemented by transiently releasing the atoms into a quasi-harmonic confinement centered between the two sites. With an appropriately chosen contact interaction strength, a controlled collision accumulates the exchange phase required for SWAP\sqrt{\mathrm{SWAP}}SWAP​ and generates entanglement. We employ a continuum, time-dependent Schrödinger-equation simulation that goes beyond a two-site Fermi--Hubbard description and benchmark it against experimentally implemented tunneling-based protocols, reproducing the observed single-particle tunneling and spin-exchange dynamics. For experimentally accessible lattice depths, we find that the proposed gate operates in ∼21 μs\sim 21\,μ\mathrm{s}∼21μs, more than an order of magnitude faster than tunneling-based implementations, while achieving fidelities ≳99%\gtrsim 99\%≳99%. We further analyze sensitivity to lattice-depth variations and show that a composite sequence improves robustness. Our results establish fast, collision-mediated entangling gates in superlattices as a promising building block for scalable neutral-atom quantum computation.
Ultracold atoms trapped in optical lattices have emerged as a scalable and promising platform for quantum simulation and computation; however, gate speeds remain a significant limitation for practical applications. In this work, we employ quantum optimal control to design fast, collision-based two-qubit gates within a superlattice based on a Fermi-Hubbard description, reaching errors in the range 10 − 3 for realistic parameters. Numerically optimizing the lattice depths and the scattering length, we effectively manipulate hopping and interaction strengths intrinsic to the Fermi-Hubbard model. Our results provide five times shorter gate durations by allowing for higher energy bands in the optimization, suggesting that standard modeling with a two-band Fermi-Hubbard model is insufficient for describing the dynamics of fast gates, and we find that four to six bands are required. Additionally, we achieve nonadiabatic gates by employing time-dependent lattice depths rather than using only fixed depths. The optimized control pulses not only maintain high efficacy in the presence of laser-intensity and phase noise but also result in negligible interwell couplings.
We demonstrate gate operations on a single qubit at a specific site without perturbing the coherence of an adjacent qubit in a 1D optical lattice when the site separation is only 532 nm. Three types of spin rotations are performed on the target qubit with fidelities between 0.88±0.05 and 0.99±0.01, whereas the superposition state of the adjacent one is preserved with fidelities between 0.93±0.04 and 0.97±0.04. The qubit is realized by a pair of Zeeman-sensitive ground hyperfine states of a ^{7}Li atom, and each site is identified by its resonance frequency in a magnetic field gradient of 1.6 G/cm. We achieve the site-specific resolving power in the frequency domain by using magic polarization for the lattice beam that allows a Fourier-limited transition linewidth as well as by highly stabilizing the lattice parameters and the ambient conditions. We also discuss a two-atom entanglement scheme using a blockade by cold collisional shifts in a 1D superlattice, for which a coherent manipulation of individual qubits is a prerequisite.
We study a dipole-dipdole collision between two atoms confined in adjacent minima of the two sublattices of an optical lattice with polarization gradient. A qubit consists of the two lowest atomic vibrational states of the optical lattice potential. The inter-atomic distance is changed adiabatically by rotating the polarization of the lasers that originate the optical lattice. In an elastic collision the two-qubit quantum states undergo controllable phase shifts that allow for the implementation of quantum gates. We obtain the truth-table for a quantum logic phase gate and calculate probability losses caused by the non-hermitian effective dipole-dipole interaction Hamiltonian.