Verification of Concurrent Quantum Protocols by Equivalence Checking

We present a tool which uses a concurrent language for describing quantum systems, and performs verification by checking equivalence between specification and implementation. In general, simulation of quantum systems using current computing technology is infeasible. We restrict ourselves to the

stabilizer

formalism, in which there are efficient simulation algorithms. In particular, we consider concurrent quantum protocols that behave

functionally

in the sense of computing a deterministic input-output relation for all interleavings of the concurrent system. Crucially, these input-output relations can be abstracted by superoperators, enabling us to take advantage of linearity. This allows us to analyse the behaviour of protocols with arbitrary input, by simulating their operation on a finite basis set consisting of stabilizer states. Despite the limitations of the stabilizer formalism and also the range of protocols that can be analysed using this approach, we have applied our equivalence checking tool to specify and verify interesting and practical quantum protocols from teleportation to secret sharing.