\indent pfaffian circuits are a new, geometrically motivated, and simplified construction of valiant's holographic algorithms. these algorithms exploit dual spinor varieties to simulate certain quantum computations (fermionic linear optics) classically, and provide a means to probe the conjectured classical-quantum boundary. combinatorial problems addressed include planar nae-sat, lattice path problems and evaluation of certain tutte polynomials. basis change is one route to superposition-like effects, and some of the geometric considerations in analyzing pfaffian circuits under arbitrary basis change will be discussed. connections are made to the sum-product algorithm, slocc equivalent entangled states, and monoidal categories.