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 <a href="http://arxiv.org/abs/quant-ph/0003035">Fortnow</a> and <a href="http://arxiv.org/abs/cs/0304008">Fenner</a>. 

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 <a href="http://arxiv.org/abs/0805.0040">this</a>. Tensor networks have also an intuitive yet precise graphical calculus as explored by <a href="http://arxiv.org/abs/quant-ph/0510032">Bob Coecke</a>, et al. which abstracts manipulations of tensor networks to operations in compact closed monoidal categories.