Entanglement-based magnetometry in a scalable ion-trap quantum processor
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Abstract
The "second quantum revolution" is coming: New fields of research, such as quantum computing and quantum metrology, are aiming at commercial applications harnessing the fundamental principles of quantum mechanics. Ion-trap experiments are at the frontier of this research because they not only enable outstanding control over single particles, but also allow for creating multi-particle entanglement.
The experiments presented in this work rely on a segmented linear Paul trap, where calcium ions are stored and employed as quantum bits. Lasers are used to carry out operations on individual qubits and to entangle multiple ions. To realize a scalable quantum computer, chains of ions can be moved and rearranged within the segmented Paul trap.
A key operation for rearranging ion chains is to separate two-ion crystals into single ions. This process is demonstrated with a minimum mean excitation of 4.16(0.16) vibrational quanta per ion at a duration of 80 µs. The most important control parameters and calibration procedures are presented in detail.
In a quantum computer, the qubit coherence time must significantly surpass the duration of gate and shuttling operations. For the Calcium-40 spin qubit employed in this thesis, temporal fluctuations of the magnetic field are the main reason for decoherence. The ion-trap apparatus is therefore enclosed in a µ-metal magnetic shield, and coils for generating the quantizing magnetic field have been replaced by Samarium–cobalt permanent magnets. These measures have substantially reduced magnetic-field fluctuations, leading to a 1/Sqrt(e) Ramsey coherence time of 370(40) ms and a spin-echo coherence time of 2.12(7) s. This is considerably longer than the typical duration of entangling gates in the 10-80 µs range.
Since ions are shuttled to different locations in the course of a quantum algorithm, the spatial variation of the magnetic field has to be taken into account as well. For this purpose, a novel measurement scheme for inhomogeneous DC magnetic fields has been developed, which operates in a previously inaccessible parameter regime in terms of spatial resolution and sensitivity. Entangled Bell states of the type |↑↓> + Exp(iϕ)|↓↑>, encoded in two ions stored at different locations, are used as sensor states. The linear Zeeman effect imprints a relative phase ϕ, which serves for measuring the magnetic-field difference ∆B between the constituent locations. Temporal magnetic-field fluctuations on both ions are rejected because of the anti-parallel spin alignment of the sensor state. Measurements of magnetic-field differences have been carried out over distances of up to 6.2 mm, with accuracies down to 310 fT, and sensitivities down to 12 pT / Sqrt(Hz). The sensing scheme features spatial resolutions of about 20 nm. A Bayesian algorithm for frequency estimation optimizes the information gain of the magnetic-field measurements while maintaining a high dynamic range.