Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)

We give a scheme for interpreting shaded tangles as quantum programs, with the property that isotopic tangles yield equivalent programs. We analyze many known quantum programs in this way—including entanglement manipulation and error correction—and in each case present a fully-topological formal verification, yielding in several cases substantial new insight into how the program works. We also use our methods to identify several new or generalized procedures.