Verification of Concurrent Quantum Protocols by Equivalence Checking

Abstract

Abstract. 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.

Towards Large-scale Functional Verification of Universal Quantum Circuits

“…Due to the absence of large, universal quantum computers and the inherent difficulty of simulating quantum circuits, testing is generally not a viable option for verification. By contrast, various methods of formal verification have been developed for quantum circuits and programs, including equivalence checking [7,30,31], diagrammatic methods [13,15], model checkers [6,16], program logics [32] and formal proof [27]. However, two questions remain: how can the intended effect of a quantum program be specified in a clear, human readable and verifiable way, and how can we scale automated verification to large circuits?…”

QPMC: A Model Checker for Quantum Programs and Protocols

“…It is worth noting that the termination properties we checked here cannot be verified by the previous tools in [1,2,11] for the following two reasons: (1) the loop program employs an amplitude damping operation which does not belong to the Clifford group; (2) the program is an open system which takes an arbitrary quantum state as its input, and we are checking the termination for any input state.…”

“…Besides the model checker proposed by Gay et al [11], recently Ardeshir-Larijani et al developed equivalence checkers for deterministic quantum protocols [1] as well as concurrent quantum protocols that behave functionally [2]. As for [11], these tools work only within the stabiliser formalism, and the generalisation to general quantum protocols seems difficult.…”

Verification of Linear Optical Quantum Computing using Quantum Process Calculus

“…When we consider the correctness of the system, we will prove that Model 1 is equivalent to the following Specification 1 process. We use the same process PolSe CT as the input for Specification 1 .…”