Consequences of Orthogonality in Quantum Simulations

The intuition from experience in low-dimensional vector spaces lacking tensor product structure is that the use of non-orthogonal basis vectors is roughly equivalent to the use of orthogonal basis vectors in a computational sense. We show that this intuition can be flawed in the case of high-dimensional spaces with tensor product structure, such as many-particle quantum systems, and the overhead which results from staying in an orthogonal many-particle basis can be enormous. This overhead is explored with some examples from quantum chemistry.