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arXiv:quant-ph/0601148 · Physical Review Letters

Quantum Manipulation of Trapped Ions in Two Dimensional Coulomb Crystals

Diego Porras, J. I. Cirac

Published Jun 29, 2006• 111 citations
arXivHTMLPDF

Abstract

We show that a large number of ions forming a 2D Coulomb crystal provides an almost ideal system for scalable quantum computation and quantum simulation. In particular, the coupling of the internal states to the motion of the ions transverse to the crystal plane allows one to implement two-qubit quantum gates. We analyze in detail the decoherence induced by anharmonic couplings, and show that very high gate fidelities can be achieved with current experimental setups.

DOI
10.1103/physrevlett.96.250501

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We show that a large number of ions forming a 2D Coulomb crystal provides an almost ideal system for scalable quantum computation and quantum simulation. In particular, the coupling of the internal states to the motion of the ions transverse to the crystal plane allows one to implement two-qubit quantum gates. We analyze in detail the decoherence induced by anharmonic couplings, and show that very high gate fidelities can be achieved with current experimental setups.
Ion trap quantum computers are based on modulating the Coulomb interaction between atomic ion qubits using external forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals by using a small and fixed number of motional modes, simplifying the scaling of ion trap quantum computers. We present analytical work that shows that gate operations need not couple to the motion of distant ions, allowing parallel entangling gates with a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also experimentally demonstrate high-fidelity entangling gates on a fully connected set of seventeen 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ qubits using simple laser pulse shapes that primarily couple to just a few modes.
Realising large-scale quantum computation in the near future will require increasing the number of low-error two-qubit gates that can be implemented on a quantum computer before decoherence. One of the biggest challenges facing current trapped ion quantum computers is implementing high-speed two-qubit operations, whilst increasing the number of qubits. One of the most promising proposals for overcoming current limitations is the use of ultra-fast pulses to implement fast two-qubit gates between nearest-neighbour pairs of ions. In this thesis, I investigate these ‘fast gates’ in two-dimensional arrays of microtraps, each containing a single ion. I argue that two-dimensional architectures allow for a significant reduction in the number of two-qubit gates required for a particular computation, as compared to one-dimensional ion chains. I demonstrate this reduction for a quantum simulation of a 40-mode Fermi-Hubbard Hamiltonian. I develop an efficient scheme that allows fast gates to be numerically optimised for two-dimensional geometries. I find that this optimisation scheme is capable of designing gates that are faster, higher fidelity, and require lower laser repetition rates. Using this scheme, I find that high-speed two-qubit gates can be optimised for two-dimensional architectures, with fidelities well above thresholds required for fault tolerant error correction, around 99.99%. Furthermore, I find that fast gates in these architectures are robust to the presence of large numbers of surrounding ions. Following previous studies [1, 2] which have identified pulse imperfections as a dominant source of error in fast gates, I perform a worst-case error analysis. I find the fast gates presented in this thesis to require very small errors in single-qubit rotations, and I present recommendations for achieving those requirements. I also investigate other experimental considerations, and make recommendations for overcoming other technical challenges in realising fast gates.
We designed and operated a surface ion trap with an ion-substrate distance of 500 μm, realized with standard printed-circuit-board techniques. The trap has been loaded with up to a few thousand Sr+ ions in the Coulomb-crystal regime. An analytical model of the pseudo-potential allowed us to determine the parameters that drive the trap into anisotropic regimes in which we obtain large (N>150) purely two dimensional (2D) ion Coulomb crystals. These crystals may open a simple and reliable way to experiments on quantum simulations of large 2D systems.
Two-dimensional (2D) ion crystals may represent a promising path to scale up qubit numbers for ion trap quantum information processing. However, to realize universal quantum computing in this system, individually addressed high-fidelity two-qubit entangling gates still remain challenging due to the inevitable micromotion of ions in a 2D crystal as well as the technical difficulty in 2D addressing. Here we demonstrate two-qubit entangling gates between any ion pairs in a 2D crystal of four ions. We use symmetrically placed crossed acousto-optic deflectors (AODs) to drive Raman transitions and achieve an addressing crosstalk error below 0.1%. We design and demonstrate a gate sequence by alternatingly addressing two target ions, making it compatible with any single-ion addressing techniques without crosstalk from multiple addressing beams. We further examine the gate performance versus the micromotion amplitude of the ions and show that its effect can be compensated by a recalibration of the laser intensity without degrading the gate fidelity. Our work paves the way for ion trap quantum computing with hundreds to thousands of qubits on a 2D ion crystal. Quantum gates in 2D ion crystals are more challenging than in 1D. Here, the authors use their 2D ion trap platform and acousto-optical deflectors to demonstrate a 2-qubit gate that can stand the ion micromotion in such configuration.
Two- or three-dimensional Paul traps can confine a large number of ions forming a Wigner crystal, which would provide an ideal architecture for scalable quantum computation except for the micromotion, an issue that is commonly believed to be the obstacle for any high-fidelity quantum gate. Here we show that the obstacle of micromotion can be overcome with current technology, even though the magnitude of the micromotion is way outside the Lamb-Dicke region. Through exact solution of the quantum Mathieu equations, we demonstrate the principle of the gate design under micromotion using two ions in a quadrupole Paul trap as an example. The proposed micromotion quantum gates can be extended to the many-ion case and may pave a new way for scalable trapped-ion quantum computation.