NP has log-space verifiers with fixed-size public quantum registers ABUZER YAKARYILMAZ Faculty of Computing University of Latvia A. C. CEM SAY Department.

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Presentation transcript:

NP has log-space verifiers with fixed-size public quantum registers ABUZER YAKARYILMAZ Faculty of Computing University of Latvia A. C. CEM SAY Department of Computer Engineering Bo ǧ aziçi University October 07, 2011 TÕRVE

VERIFIER PROVER An interactive proof system for a language probabilistic machine

VERIFIER PROVER unlimited computational power Prover can cheat! resource-bounded An interactive proof system for a language

Two criteria:

Arthur-Merlin system (space-bounded) ₵01#…01#$ …#01#… Work tape (restricted) 1 Communication cell Random number generator Input tape (read-only) …#11#… Work tape (unlimited) outcomes ARTHUR MERLIN

Complexity classes

A new system: q A M ₵01#…01#$ …#01#… Work tape (restricted) 1 Communication cell A finite quantum register Input tape (read-only) …#11#… Work tape (unlimited) outcomes Â RTHUR MERLIN

The finite quantum register

The operations on the register … … … …

Some details of the algorithm ₵01…1#10…1#… 11…0#$ auxiliary value Initial state Before reading $ reject

Concluding remarks

References