Here's a quantum computer simulator [1] I wrote years ago that allows you to construct quantum circuits using the most common quantum gates found in literature. This is all done by the application of complex matrices. On the right there is the probability distribution that taking a measurement would result in.
[1] https://github.com/qcsimulator/qcsimulator.github.io
Edit: It's worth noting that we can study quantum computing without a quantum computer, just as we can study computing without a classical computer.
Edit 2: Here's Grover's Algorithm in my simulator where you can see that the probability of measuring the correct "hidden" oracle value is 96% after only three applications of the diffusion operator: https://qcsimulator.github.io/?example=Grover%27s%20Algorith...
Furthermore, the bifurcation of computer science and electrical engineering hasn't been all that successful as an academic practice. UC Berkeley recently decided to leave the ABET accreditation process for EECS because they felt they can innovate on a better synthesis of the fields for the fields and students.
And similarly, studying QC in the theoretical form can also lead to discovery and understanding of quantum properties. Even if we have no fully-featured quantum computers.
Computer science and the construction of computers are virtually the same thing. Making a computer was never a challenge; making a faster computer always is.
Some of it will be encompassed by computer science in that algorithms will still have the same metrics, but there may be other metrics for which to study quantum algorithms.