Distilled to its linear algebraic core, Quantum Computing can be presented and understood in a completely physics-free way easily accessible to Computer Scientists. Two papers taking this point of view are Fortnow and Fenner.
Driving this linear algebraic point of view even further, one can see multilinear algebra, which deals with the contraction of tensor networks as a core concept, as fundamental. It suffices to model quantum computing, simulation of quantum systems (Projected Entangled Pair States, or PEPS), statistical mechanical models (partition functions), etc. A good text to get started is probably this. Tensor networks have also an intuitive yet precise graphical calculus as explored by Bob Coecke, et al. which abstracts manipulations of tensor networks to operations in compact closed monoidal categories.