Distinguishing Short Quantum Computations

TL;DR

This paper proves that distinguishing short quantum computations is a complete problem for the class QIP, with implications for quantum algorithm verification, by reducing QIP problems to logarithmic depth circuits.

Contribution

It introduces a reduction technique showing that the distinguishability problem remains QIP-complete even for logarithmic depth quantum circuits.

Findings

Distinguishing short quantum circuits is QIP-complete.

QIP remains complete for constant depth circuits with unbounded fan-out.

Reduction techniques enable complexity classification of shallow quantum computations.

Abstract

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.