[kvathupo]

They're not easily comparable since quantum complexity refers to the upper bound on queries to some black-box "quantum oracle", which exists on the gate-level. A classical parallel would perhaps be queries to a translation lookaside buffer, which can be regarded as a gate-level black-box (I'm sure people who actually work in hardware already smell blood!).

By contrast, classical complexity, as in sorting algorithms, is reasoned about in higher-level programming languages, whose operational complexity is hard to describe down to the bit-level.

I'm curious if anyone more knowledgeable could argue one-way-or-another if this is a boon to the quantum-computers-will-probably-be-faster-in-realization camp.

[adastra22]

I am also relatively new to this, but I believe there is an apples-to-apples comparison with the number of gate operations required to solve an instance of a problem.