Definitely not. Quantum computing building blocks do not have anything that makes them inherently easier to miniaturize: quite the opposite, there is enormous amount of classical hardware necessary to support a single quantum bit. Moreover, some form of "isolation" between the qubits is necessary, so you can not just pack them together.

Current sizes of quantum bits: cavities are cm to mm scale; transmons and photonics can be much smaller, but nowhere near the size of modern transistors; ions need to be trapped in something and usually the scale is not better than the other options.

There is the hope that qubits can be made in silicon and use lithographic technologies, but then at best we will reach the density of current CPUs (but such a thing is science fiction at the moment).

It hard to know if that theory is going to translate into reality. The machinery required for isolating the qubits, configuring the qubits for a computation, and reading out the qubits at the end may prevent very much scaling.

Science fiction has hypothesized about quantum computing that involves macroscopically-sized bits of carefully constructed matter running a number of qubits best described with scientific notation, but it's not clear how one would set up problems or read anything out of such a thing.