Formal verification of higher dimensional quantum protocols
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916412059025408 |
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| author | Puthoor, Ittoop Vergheese |
| author_facet | Puthoor, Ittoop Vergheese |
| contents | Formal methods have been a successful approach for modelling and verifying the correctness of complex technologies like microprocessor chip design, biological systems and others. This is the main motivation of developing quantum formal techniques which is to describe and analyse quantum information processing systems. Our previous work demonstrates the possibility of using a quantum process calculus called Communicating Quantum Processes (CQP) to model and describe higher dimensional quantum systems. By developing the theory to generalise the fundamental gates and Bell states, we have modelled quantum qudit protocols like teleportation and superdense coding in CQP. In this paper, we demonstrate the use of CQP to analyse higher dimensional quantum protocols. The main idea is to define two processes, one modelling the real protocol and the other expressing a specification, and prove that they are behaviourally equivalent. This is a work-in-progress and we present our preliminary results in extending the theory of behavioural equivalence in CQP to verify higher dimensional quantum protocols using qudits. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_17980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formal verification of higher dimensional quantum protocols Puthoor, Ittoop Vergheese Formal Languages and Automata Theory Quantum Physics Formal methods have been a successful approach for modelling and verifying the correctness of complex technologies like microprocessor chip design, biological systems and others. This is the main motivation of developing quantum formal techniques which is to describe and analyse quantum information processing systems. Our previous work demonstrates the possibility of using a quantum process calculus called Communicating Quantum Processes (CQP) to model and describe higher dimensional quantum systems. By developing the theory to generalise the fundamental gates and Bell states, we have modelled quantum qudit protocols like teleportation and superdense coding in CQP. In this paper, we demonstrate the use of CQP to analyse higher dimensional quantum protocols. The main idea is to define two processes, one modelling the real protocol and the other expressing a specification, and prove that they are behaviourally equivalent. This is a work-in-progress and we present our preliminary results in extending the theory of behavioural equivalence in CQP to verify higher dimensional quantum protocols using qudits. |
| title | Formal verification of higher dimensional quantum protocols |
| topic | Formal Languages and Automata Theory Quantum Physics |
| url | https://arxiv.org/abs/2409.17980 |