I want to preface with a disclaimer that I am a physicist with minimal knowledge of computer hardware. I have a solid understanding of quantum information from a theoretical standpoint but zero knowledge of how it is implemented. Here goes...
When a company boasts that there newest chip has $X$ qubits, what exactly does that mean? Should I think of $X$ as being analogous with 32 or 64 bits on a conventional processor, meaning that the quantum computer can hold and process data types of size $X$? Or is $X$ something physical, like the number of Josephson junctions on the chip? should I think of $X$ as being equivalent to the number of transistors on a conventional processor? The benchmark of a conventional microprocessor is the number of transistors, so it is tempting to make the equivalence between transistor and qubit but I don't think that is correct because qubit is a unit of information and a transistor is a hardware thing. And furthermore I would not understand how quantum supremacy could be achieved with only ~50 qubits when conventional processors have billions of transistors. It just seems strange to say that a chip has $X$ 'qubits', because from a theoretical standpoint a qubit is information and not hardware.
I am realizing that my confusion boils down to memory vs processing power. I get that in order to store $2^X$ states, I would need $X$ physical qubits (Josephson junctions, spin states, etc). But then where does the processing power come from? On a conventional chip, you have registers to store the information to be processed, but then a ton of transistors to perform the computation. My question is how this processing power is measured in a quantum computer? Do the number of quantum gates on the chip really not matter as much as the number of qubits they are capable of operating on?