Abstract
We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the common coset range property of two functions having identical ranges within each coset of some normal subgroup.
Research partially supported by the EU 5th framework programs RESQ IST-2001-37559 and RAND-APX IST-1999-14036, and by CNRS/STIC 01N80/0502 and 01N80/0607 grants, by ACI Cryptologie CR/02 02 0040 grant of the French Research Ministry, and by OTKA T42559, T42706, and NWO-OTKA N34040 grants.
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Friedl, K., Magniez, F., Santha, M., Sen, P. (2003). Quantum Testers for Hidden Group Properties. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_36
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DOI: https://doi.org/10.1007/978-3-540-45138-9_36
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