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Do the latest D-Wave machines use compounds of $\require{\mhchem}\ce{^{3}He}$ and $\ce{^{4}He}$ for cooling? If not, how does D-Wave approach cooling its plates low enough to achieve superconductivity? What compounds does DWave use for the plates in their fridge, and at what temperature do its plates reach superconductivity?

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Yes, they use $\require{\mhchem}\ce{^3He}$ and $\ce{^4He}$. No, they do not use compounds of these but instead a solution of these two (at the operating temperature) liquid nobel gases. The details can be found in the wikipedia article on dilution refrigerators.

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