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Symbolic model checking quantum circuits in Maude.

Canh Minh Do¹, Kazuhiro Ogata¹

¹School of Information Science, Japan Advanced Institute of Science and Technology, Asahidai, Nomi, Ishikawa, Japan.

Peerj. Computer Science

|July 10, 2024

Summary

This summary is machine-generated.

This study introduces a symbolic method for model checking quantum circuits, verifying quantum communication protocols using Maude and linear temporal logic (LTL). The approach enables formal specification and automated verification of quantum circuit correctness.

Keywords:

Dirac notation Maude Quantum circuits Symbolic model checking

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Area of Science:

Quantum Information Science
Formal Methods
Computer Science

Background:

Quantum circuits require formal verification methods to ensure correctness.
Existing methods may not be suitable for symbolic analysis of quantum protocols.
High-level specification languages can aid in formalizing quantum computations.

Purpose of the Study:

To present a symbolic approach for model checking quantum circuits.
To implement this approach using the Maude system.
To formally verify the correctness of several quantum communication protocols.

Main Methods:

Utilizing laws from quantum mechanics and matrix operations with Dirac notation for symbolic representation.
Implementing the symbolic approach in Maude, a rewriting logic-based system.
Employing linear temporal logic (LTL) for property specification and Maude's built-in LTL model checker for verification.

Main Results:

Successfully formally specified and verified several quantum communication protocols, including Superdense Coding and Quantum Teleportation.
Demonstrated the feasibility of using Maude for symbolic model checking of quantum circuits.
The approach allows describing quantum circuits as sequences of gate/measurement applications.

Conclusions:

The proposed symbolic approach is a viable first step towards a general framework for formal specification and verification of quantum circuits in Maude.
Automated verification of quantum protocols is achievable using this method.
The framework supports specifying initial states and desired properties in LTL.