Distinguishing Short Quantum Computations

Distinguishing logarithmic depth quantum circuits on mixed states is shown to be complete for QIP, the class of problems having quantum interactive proof systems. Circuits in this model can represent arbitrary quantum processes, and thus this result has implications for the verification of implementations of quantum algorithms. The distinguishability problem is also complete for QIP on constant depth circuits containing the unbounded fan-out gate. These results are shown by reducing a QIP-complete problem to a logarithmic depth version of itself using a parallelization technique.