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Bulletin of the American Physical Society

Trapped-Ion Quantum Simulations of Spin Systems: From Two Qubits to Thousands

Warren E. Lybarger, Dana J. Berkeland, John Chiaverini

Published Mar 10, 2008• 1 citation
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Trapped ions, trapped atoms, and NMR spin systems are all fine ways of building small “toy” quantum computers, each with its own advantages and disadvantages. There are also many other techniques which have been suggested, although these three so far remain in the lead for general-purpose quantum computing. However, the most powerful general-purpose quantum computers constructed to date have only about a dozen qubits, and this is not nearly large enough to make quantum computers useful rather than merely interesting. (Larger systems have been used to demonstrate particular quantum information processing techniques, but these cannot as yet be used to implement arbitrary quantum algorithms.) Although it is not completely clear how complex a general-purpose quantum computer needs to be, it is clear that such a device will involve thousands or even millions of qubits, rather than the dozens involved today. It is, therefore, important to consider whether there is any hope of scaling up these technologies to useful sizes, and we will consider each of the three approaches in turn, before turning briefly to alternative technologies which have not been discussed so far. Trapped ions Trapped ions initially look very promising as a candidate for scaling up, as it is possible to trap thousands of ions while keeping a reasonable distance between them. Early experiments relied on particular tricks which only work with systems of two ions, but this is not true of more recent work, and there is no reason in principle why these large strings of ions could not be controlled.
We propose a hardware architecture and protocol for connecting many local quantum processors contained within an optical cavity.The scheme is compatible with trapped ions or Rydberg arrays, and realizes teleported gates between any two qubits by distributing entanglement via single-photon transfers through a cavity.Heralding enables high-fidelity entanglement even for a cavity of moderate quality.For processors composed of trapped ions in a linear chain, a single cavity with realistic parameters successfully transfers photons every few μs, increasing the interchain entanglement rate over 2 orders of magnitude beyond current methods and eliminating a major bottleneck for scaling trapped-ion systems.For one realistic scenario, we outline how to achieve the any-to-any entanglement of 20 ion chains containing a total of 500 qubits in 200 μs, with both fidelities and rates limited only by local operations and ion readout.For processors composed of Rydberg atoms, our method fully connects a large array of thousands of neutral atoms.The connectivity afforded by our architecture is extendable to tens of thousands of qubits using multiple overlapping cavities, expanding capabilities for noisy intermediate-scale quantum era algorithms and Hamiltonian simulations, as well as enabling more robust high-dimensional error-correcting schemes.
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.