1 research outputs found
Stabilizer Circuits, Quadratic Forms, and Computing Matrix Rank
We show that a form of strong simulation for -qubit quantum stabilizer
circuits is computable in time, where is the
exponent of matrix multiplication. Solution counting for quadratic forms over
is also placed into time. This improves previous
bounds. Our methods in fact show an -time reduction from
matrix rank over to computing (hence also to solution counting) and a converse reduction
that is except for matrix multiplications used to decide whether
. The current best-known worst-case time for matrix rank is
over , indeed over any field, while is
currently upper-bounded by Our methods draw on properties of
classical quadratic forms over . We study possible distributions
of Feynman paths in the circuits and prove that the differences in vs.
counts and vs. counts are always or a power of . Further
properties of quantum graph states and connections to graph theory are
discussed.Comment: Main change is to conclusion section: more information about relation
to matroids and the generalized Tutte polynomia