This paper presents a symbolic approach to model checking quantum circuits by using a set of laws from quantum mechanics and basic matrix operations with Dirac notation.We use Maude, a high-level specification/programming language based on rewriting logic, to implement our symbolic approach.As a case study, we use the approach to formally specify and verify the correctness of the quantum teleportation protocol, which is an important quantum communication protocol in the early work of quantum communications.Moreover, our implementation can be used as a general framework to formally specify and verify quantum circuits in Maude in an effortless way, where only an initial quantum state and a sequence of actions describing how a quantum circuit works in a simple way are required.
This paper presents a symbolic approach to model checking quantum circuits by using a set of laws from quantum mechanics and basic matrix operations with Dirac notation.We use Maude, a high-level specification/programming language based on rewriting logic, to implement our symbolic approach.As a case study, we use the approach to formally specify and verify the correctness of the quantum teleportation protocol, which is an important quantum communication protocol in the early work of quantum communications.Moreover, our implementation can be used as a general framework to formally specify and verify quantum circuits in Maude in an effortless way, where only an initial quantum state and a sequence of actions describing how a quantum circuit works in a simple way are required.
This article presents a symbolic approach to model checking quantum circuits using a set of laws from quantum mechanics and basic matrix operations with Dirac notation. We use Maude, a high-level specification/programming language based on rewriting logic, to implement our symbolic approach. As case studies, we use the approach to formally specify several quantum communication protocols in the early work of quantum communication and formally verify their correctness: Superdense Coding, Quantum Teleportation, Quantum Secret Sharing, Entanglement Swapping, Quantum Gate Teleportation, Two Mirror-image Teleportation, and Quantum Network Coding. We demonstrate that our approach/implementation can be a first step toward a general framework to formally specify and verify quantum circuits in Maude. The proposed way to formally specify a quantum circuit makes it possible to describe the quantum circuit in Maude such that the formal specification can be regarded as a series of quantum gate/measurement applications. Once a quantum circuit has been formally specified in the proposed way together with an initial state and a desired property expressed in linear temporal logic (LTL), the proposed model checking technique utilizes a built-in Maude LTL model checker to automatically conduct formal verification that the quantum circuit enjoys the property starting from the initial state.
We describe model-checking techniques for protocols arising in quantum information theory and quantum cryptography. We discuss the theory and implementation of a practical model checker, QMC, for quantum protocols. In our framework, we assume that the quantum operations performed in a protocol are restricted to those within the stabilizer formalism; while this particular set of operations is not universal for quantum computation, it allows us to develop models of several useful protocols as well as of systems involving both classical and quantum information processing. We discuss the modeling language of QMC, the logic used for verification, and the verification algorithms that have been implemented in the tool. We demonstrate our techniques with applications to a number of case studies, including quantum teleportation and the BB84 quantum coin-flipping protocol. 11.1 Introduction Model-checking is a method of computer-aided verification used widely in both academia and industry for the analysis of software and communication systems. The method essentially consists of three phases: (1) modeling the system of interest at a suitable level of abstraction, usually by describing it in a formal specification language; (2) specifying the properties that the system must satisfy – these properties are typically expressed with reference to the system model, using a logic designed specially for this purpose ( e.g. , linear or branching time temporal logic); and (3) supplying the model and the properties to a model-checking tool, which automatically constructs the state space of the model and checks whether or not the given properties are satisfied (and if not, usually providing a counterexample).
We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using present-day technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of PRISM, a probabilistic model-checking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniques by modelling a selection of quantum protocols (namely superdense coding, quantum teleportation, and quantum error correction) and verifying their basic correctness properties. Our results provide a foundation for further work on modelling and analysing larger systems such as those used for quantum cryptography, in which basic protocols are used as components.
Quantum computing uses the laws of quantum mechanics to perform computation. Information is stored in qubits and processed using quantum gates arranged as quantum circuits. As quantum hardware grows in size and complexity, verifying these systems becomes increasingly difficult. Traditional verification methods do not scale well and quickly become computationally infeasible. This creates a strong need for more powerful and scalable verification techniques. Formal methods provide a potential solution to this problem. Techniques such as theorem proving, model checking, and symbolic reasoning offer mathematically rigorous ways to verify correctness, equivalence, and implementation. They also help detect design errors early in the development process. This review examines how formal methods are applied to quantum circuit verification. It focuses on barrier certificates, abstract interpretation, model checking, theorem proving approaches. The review discusses both the theoretical foundations and practical applications of these techniques. Their strengths and limitations are analysed through representative case studies. Finally, the review highlights open challenges and identifies promising directions for future research. An extensive set of references is included to support further study and exploration.
Quantum computing uses the laws of quantum mechanics to perform computation. Information is stored in qubits and processed using quantum gates arranged as quantum circuits. As quantum hardware grows in size and complexity, verifying these systems becomes increasingly difficult. Traditional verification methods do not scale well and quickly become computationally infeasible. This creates a strong need for more powerful and scalable verification techniques. Formal methods provide a potential solution to this problem. Techniques such as theorem proving, model checking, and symbolic reasoning offer mathematically rigorous ways to verify correctness, equivalence, and implementation. They also help detect design errors early in the development process. This study examines how formal methods are applied to quantum circuit verification. It focuses on barrier certificates, abstract interpretation, model checking, and theorem proving approaches. The study discusses both the theoretical foundations and practical applications of these techniques. Their strengths and limitations are analysed through representative case studies. Finally, the study highlights open challenges and identifies promising directions for future research. An extensive set of references is included to support further study and exploration.
Quantum circuit compilation is a crucial step in translating high-level quantum algorithms into executable quantum circuits on specific hardware. The complexity and potential for errors within this process necessitate rigorous verification methods. This paper proposes a novel approach leveraging symbolic execution to formally verify quantum circuit compilation. We represent quantum circuits and compilation steps as a symbolic program, enabling the exploration of all possible compilation paths. By incorporating quantum gate fidelities and noise models into the symbolic execution engine, we can identify potential errors in the compilation logic, providing a robust and systematic way to ensure the correctness of the compilation process. The core claim is that symbolic execution can be extended to formally verify the correctness of quantum circuit compilation processes. This work addresses a critical need in quantum computing, offering a new technique for building trust and reliability into quantum software.