The most often quoted size parameter for Quantum Computers is how many Qubits they implement. But ultimately (at least in some hypothetical application), these Qubits are intended to perform calculations, including Toffoli gates.
How many Toffoli gates are executed in quantum computations performed by modern, currently existing Quantum Computers ?
In practice, I'm not sure any deployed algorithms are using Toffolis; with the quality of quantum devices today it makes more sense to adapt an algorithm to what's natural for the hardware (a Toffoli is natural for binary computations, not physical deployments). In theory, a modern quantum computer could likely do between 1 and 8.
For the lower bound: here's a paper form 2008 experimentally demonstrating one Toffoli on trapped ions: https://arxiv.org/abs/0804.0082
For the upper bound: checking IBM's live data, they have qubit coherence times of almost 1 ms, and their CZ gates take 20-40 ns. This means they could do at most 25-50 CZ gates sequentially. Looking at a circuit diagram for a Toffoli, the best I can find is 6 sequential 2-qubit gates (with some other 1 qubit gates in between; to be generous, I'll assume they are effectively instant or can be compiled away). Dividing the range [25,50] by 6 gives [4,8] if we round down. I think most systems these days are comparable in coherence times and fidelity to IBM's.
But broadly I think there's an X-Y problem in your question. You're probably interested in when quantum computers can perform meaningful calculations at scale. For that, no one expects Toffolis directly on the raw physical qubits; instead we expect error correction, and then we do Toffolis on the error corrected qubits. The progress on that front is that Google demonstrated 1 error-corrected qubit (...more or less, I think they didn't even claim it to be a full logical qubit): https://www.nature.com/articles/s41586-024-08449-y. It will be awhile before anyone demonstrates even a single Toffoli in an error-corrected code, as it requires significantly more resources (Fig 24 in https://arxiv.org/abs/2409.17595 shows 8 logical qubits of workspace for the Toffoli, so you'd need 8+3 inputs = 11 in total, and I think a larger code than Google's results, so that translates to probably 1000+ physical qubits to even think about doing one).
