D6.18 QPSA Quantum Walks and Markov
Creators: name: Hibti, Mohamed
name: Zaiou, Ahmed
Publisher: name: Zenodo
Year: 2023
Subjects: Quantum walks
Dynamic Safety Assessment
Markov Graphs
Sequence identification

description: In this work, we present a quantum walks based approach for Probabilistic Safety Assessment problems in the dynamic Markovian framework. After presenting well known quantum walk algorithms for detecting or finding marked elements in a graph or for finding paths in specific graphs, we propose two algorithms to address the more general problem of finding paths from some point to marked elements. The first algorithm is based on move and store strategy to built failure sequences from an initial state to the marked states. It uses a full register assembling qubits representing components of the system under study and other control and ancilla qubits (between n and 2n) to identify all the sequences. The second algorithm is based on a hybrid approach to consider di˙erent cascading circuits for solving relatively large instances. We present some tests on a Qiskit simulation library that were performed to compare our algorithms against classical random walks. These tests showed that classical approach has advances in the first iteration but the hybrid approach scales better in the sense that it identifies a large number of paths and converges towards all the possible paths to these marked vertices.
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