LVC Mathematical Physics Research Group
Background Notes 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.