(Un)decidable problems about reachability of quantum systems
- Publisher:
- Springer
- Publication Type:
- Conference Proceeding
- Citation:
- Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2014, 8704 LNCS, pp. 482-496
- Issue Date:
- 2014-01-01
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We study the reachability problem of a quantum system modeled by a quantum automaton, namely, a set of processes each of which is formalized as a quantum unitary transformation. The reachable sets are chosen to be boolean combinations of (closed) subspaces of the state Hilbert space of the quantum system. Four different reachability properties are considered: eventually reachable, globally reachable, ultimately forever reachable, and infinitely often reachable. The main result of this paper is that all of the four reachability properties are undecidable in general; however, the last three become decidable if the reachable sets are boolean combinations without negation. © 2014 Springer-Verlag.
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