Background Requirements for Undergraduate Researchers
The minimum background for undergraduate students to begin research in quantum information science is a linear algebra course and some "mathematical maturity." Essential linear algebra background includes the spectral theorem, at least for diagonalization of hermitian and unitary operators on complex vector spaces.
To bridge the gap between an introductory linear algebra course and really working on problems in quantum information, we use Nielsen and Chuang's text together with background notes that we have produced. Our students spend the first two weeks of their summer project working through Chapter 2 of Nielsen and Chuang and our background notes on the essentials of matrix groups, their Lie algebras, and group and algebra actions on vector spaces and tensor products.
We have used versions of our background notes since 2002. We revise and update each year. Please contact us if you would be interested in having a copy.
Software for Stabilizer Calculations
We and our students have written code in Mathematica and GAP for computations involving pure and mixed states, partial trace, local unitary stabilizer, and Pauli stabilizer calculations. Development is ongoing. Please contact us if you would be interested in trying our latest versions.