Automated verification techniques for quantum computers

Abstract

Quantum computing has become a field with high interest in both academia and industry due to recent advances in the development of quantum computers. Whilst these devices may provide speedups to solving certain problems in the future, there are still several issues to address. This thesis explores the automated verification of different aspects of quantum computers. Quantum computers are more complex than classical computers and so the verification techniques that are commonly used classically need to be adapted for the quantum domain. In this thesis, two techniques are adapted to handle the verification of quantum computers. Firstly, SilVer is presented as an automated tool for checking quantum programs written in the high-level programming language Silq. SilVer converts Silq programs into a model that is based on quantum RAM (QRAM) devices, allowing for representation of both quantum and classical operations. User-defined specification are used to encode the desired behaviour of a program. This model and specification are automatically converted into proof obligations that are checked using a Satisfiability Modulo Theory (SMT) solver. Several case studies are provided with their setup and verification run times. Secondly, the usage of barrier certificates as a verification technique for quantum computers is explored. Barrier certificates are a technique used in control theory to check if a dynamical system enters an unsafe region or not. Quantum computers are based on dynamical systems and so barrier certificates can be used to reason about their safety. Barrier certificates are adapted to handle complex variables and different quantum systems. Computational methods are provided for generating barrier certificates given a quantum system and its specification. Case studies are provided to explore the usage of barrier certificates for quantum computing