# The Power of a Single Qubit: Two-way Quantum Finite Automata and the Word Problem

@inproceedings{Remscrim2020ThePO, title={The Power of a Single Qubit: Two-way Quantum Finite Automata and the Word Problem}, author={Zachary Remscrim}, booktitle={ICALP}, year={2020} }

The two-way finite automaton with quantum and classical states (2QCFA), defined by Ambainis and Watrous, is a model of quantum computation whose quantum part is extremely limited; however, as they showed, 2QCFA are surprisingly powerful: a 2QCFA, with a single qubit, can recognize, with bounded error, the language $L_{eq}=\{a^m b^m :m \in \mathbb{N}\}$ in expected polynomial time and the language $L_{pal}=\{w \in \{a,b\}^*:w \text{ is a palindrome}\}$ in expected exponential time.
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