We're able to see a lot of things using computers that we can't see normally: yellow-green, UV light, X-rays, etc. What do we have that harnesses the ability to "see" what dogs smell (e.g., harnessing a dog's sense of smell to detect cancer and so forth)?
NMR spectroscopy is a technology that is used to identify molecules. So-called "NMR spectra catalogs" document the spectra of various known compounds. Acquiring these spectra requires purified samples, expensive equipment, and time. In addition to making next-generations of this technology into something that would be practical for realtime "smelling", you'd have to match up catalog entries with what dogs actually respond to. That's going to take a fair bit of work.
There's some literature online about growing olfactory sensory neurons in a Petri dish (with difficulty). If we can learn how the signaling pathways work for "odorant detection" for specific odorants or "fragrances" that we already know dogs perceive, perhaps we could genetically engineer a cultured neuron cell to "light up" a fluorescent marker or issue some other signal that is perceptible to humans, whenever some dog-specific odor wafts in. I suspect this would be more realistic than "tabletop NMR" in our lifetime.
Warwick University's e-nose technology has been around for quite a while: https://warwick.ac.uk/fac/sci/eng/research/impact/electronicnose/
As far as I understand their technology, they sample gas, and analyse it using a solid state CMOS device to generate a signature signal for particular compounds/mixtures. The devices have been used in a variety of industrial gas sensing applications.
There has been some progress in using e-noses in medical diagnosis, for instance this paper reports the use of e-noses to sample volatile organic compounds from urine in type 2 diabetes diagnosis: https://www.ncbi.nlm.nih.gov/pubmed/30513787
The difference from NMR is that e-noses don't generally try to identify specific molecules, but rather, to generate a signature for a particular organic compound or complex mixture, which can then be compared with other signatures from other samples using a machine-learning approach.