At its most fundamental level, circuit-based quantum computation relies on the application of controlled phase shift operations on quantum registers. While these operations are generally compromised by noise and imperfections, quantum gates based on geometric phase shifts can provide intrinsically fault-tolerant quantum computing. Here we demonstrate the high-fidelity realization of a recently proposed fast (non-adiabatic) and universal (non-Abelian) holonomic single-qubit gate, using an individual solid-state spin qubit under ambient conditions. This fault-tolerant quantum gate provides an elegant means for achieving the fidelity threshold indispensable for implementing quantum error correction protocols. Since we employ a spin qubit associated with a nitrogen-vacancy colour centre in diamond, this system is based on integrable and scalable hardware exhibiting strong analogy to current silicon technology. This quantum gate realization is a promising step towards viable, fault-tolerant quantum computing under ambient conditions.
Nitrogen-vacancy (NV) color centers in nanodiamonds are highly promising for bioimaging and sensing. However, resolving individual NV centers within nanodiamond particles and the controlled addressing and readout of their spin state has remained a major challenge. Spatially stochastic superresolution techniques cannot provide this capability in principle, whereas coordinate-controlled super-resolution imaging methods, like stimulated emission depletion (STED) microscopy, have been predicted to fail in nanodiamonds.Here we show that, contrary to these predictions, STED can resolve single NV centers in 40À250 nm sized nanodiamonds with a resolution of ≈10 nm. Even multiple adjacent NVs located in single nanodiamonds can be imaged individually down to relative distances of ≈15 nm. Far-field optical super-resolution of NVs inside nanodiamonds is highly relevant for bioimaging applications of these fluorescent nanolabels. The targeted addressing and readout of individual NV À spins inside nanodiamonds by STED should also be of high significance for quantum sensing and information applications.
Nitrogen vacancy (NV) NV centers in diamond are now the leading modality for nanoscale magnetic sensing, with wide-ranging applications in both the physical and life sciences, including the use of single NV center probes for imaging of magnetic vortices [1] and spin waves [2] in condensed matter systems as well as single proton magnetic resonance imaging (MRI) [3]; and the use of ensembles of NV centers for wide-field magnetic field imaging of biological cells [4,5] and geoscience samples [6]. Many envisioned applications of NV centers at the nanoscale, such as determining atomic arrangements in single biomolecules [3] or realizing selective strong coupling between individual spins [7] as a pathway to scalable quantum simulations [8], would benefit from a combination of superresolution imaging techniques with high sensitivity NV magnetometry. Recently, mapping the position of multiple NV centers has been improved beyond the diffraction limit by techniques using magnetic field gradients [9-11], which locally shift the NV center resonances but can deteriorate the sample to be probed. Alternatively, far-field optical superresolution techniques have the advantage of being versatile, simple to integrate into standard NV-diamond microscopes, require no special fabrication technique or magnetic field gradients, are compatible with a wide range of NV sensing techniques, and allow for fast switching between multiple NV centers. Coordinate-stochastic superresolution imaging methods, namely STochastic Optical Reconstruction Microscopy (STORM) and Photo Activated Localization Microscopy (PALM), readily offer high parallelization in sparse samples, but are prone to artefacts at high emitter densities and have been implemented until now only for a few NV centers per diffraction limited volume [12,13]. On the other hand, coordinate-deterministic superresolution methods provide targeted probing of individual NV spins with nanometric resolution [14][15][16], which is well suited for the purpose of coherent nanoscale AC magnetometry, where each NV acts as a local phase-controlled magnetometer probe.In this letter, we demonstrate the capability of spin-RESOLFT (REversible Saturable OpticaL Fluorescence Transitions), a coordinate-deterministic technique for combined far-field optical imaging and coherent spin manipulation, to map spatially varying magnetic fields at the nanoscale, including the NMR signal from external nuclear spins. Importantly, spin-RESOLFT does not require multi-wavelength excitation and high optical powers, as typically used with STimulated Emission Depletion (STED) [17] microscopy or Ground State Depletion (GSD) by metastable state pumping [18]. As shown below, we use spin-RESOLFT to optically resolve individual NV centers with a resolution of about 20 nm in the lateral (xy) directions, while exploiting the spin-state dependent optical properties ( Fig. 1(a)) and long electronic spin coherence times of NV centers in bulk diamond for precision magnetic field sensing. Moreover, we show that the localization ...
Understanding the physical origin of noise affecting quantum systems is important for nearly every quantum application. Quantum noise spectroscopy has been employed in various quantum systems, such as superconducting qubits, NV centers and trapped ions. Traditional spectroscopy methods are usually efficient in measuring noise spectra with mostly monotonically decaying contributions. However, there are important scenarios in which the noise spectrum is broadband and non-monotonous, thus posing a challenge to existing noise spectroscopy schemes. Here, we compare several methods for noise spectroscopy: spectral decomposition based on the Carr-Purcell-Meiboom-Gill (CPMG) sequence, the recently presented DYnamic Sensitivity COntrol (DYSCO) sequence and a modified DYSCO sequence with a Gaussian envelope (gDYSCO). The performance of the sequences is quantified by analytic and numeric determination of the frequency resolution, bandwidth and sensitivity, revealing a supremacy of gDYSCO to reconstruct non-trivial features. Utilizing an ensemble of nitrogen-vacancy centers in diamond coupled to a high density 13 C nuclear spin environment, we experimentally confirm our findings. The combination of the presented schemes offers potential to record high quality noise spectra as a prerequisite to generate quantum systems unlimited by their spin-bath environment.arXiv:1803.07390v3 [quant-ph]
Geometric phases 1 and holonomies 2, 3 (their non-commuting generalizations) are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against noise and experimental imperfections. Despite their conceptual appeal and proven fault-tolerance 4-6 , for a long time their practical use in quantum computing was limited to proof of principle demonstrations. Only in 2012 Sjöqvist et al. 7 formulated a strategy to generate non-Abelian (i.e. holonomic) quantum gates through non-adiabatic transformation. Successful experimental demonstrations of this concept followed on various physical qubit systems [8][9][10][11] and proved the feasibility of this fast, holonomic quantum gate concept. Despite these successes, the experimental implementation of such non-Abelian quantum gates remains experimentally challenging since in general the emergence of a suitable holonomy requires encoding of the logical qubit within a three (or higher) level system being driven by two (or more) control fields. A very recent proposal by Liang et al. 12 offers an elegant solution generating a non-Abelian, geometric quantum gate on a simple, two-level system driven by one control field. Exploiting the concept of transitionless quantum driving 13 it allows the generation of universal geometric quantum gates through superadiabatic evolution. This concept thus generates fast and robust phase-based quantum gates on the basis of minimal experimental resources. Here, we report on the first such implementation of a set of non-commuting single-qubit superadiabatic geometric quantum gates on the electron spin of the negatively charged nitrogen vacancy center in diamond. The realized quantum gates combine high-fidelity and fast quantum gate performance. This provides a promising and powerful tool for large-scale quantum computing under realistic, noisy experimental conditions.
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