1. 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

2. VERIFIER PROVER An interactive proof system for a language probabilistic machine

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

4. Two criteria:

5. 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

6. Complexity classes

7. 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  RTHUR MERLIN

8. The finite quantum register

9. The operations on the register … … … …

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

13. Concluding remarks

14. References