Are circuits with more than 1000 gates common?

Question

I have seen circuits with 30 qubits and around 500 gates. Also circuits with 32 qubits and 6000 gates. Are circuits with more than 1000 gates common in quantum computing? Are there many quantum algorithms that require more than 1000 gates? How common are they?

Answer 1

I'd say it's far more common for quantum algorithms to use billions of gates than thousands. And that's assuming you're ignoring Clifford gates as well as error correction overhead! If you want to count those, add in another factor of a million.

For example...

According to Table III of https://arxiv.org/abs/2011.03494 , quantum chemistry algorithms looking at properties of the FeMoCo molecule use half a billion Toffoli gates.

According to Table 1 of https://arxiv.org/abs/1905.09749 , factoring 2048 bit numbers takes 3 billion Toffoli gates:

According to Table 1 of https://arxiv.org/abs/2001.09580 , 256 bit elliptic curve discrete logarithms take a few billion T gates: