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On the power of quantum finite state automata
- Attila Kondacs, J. Watrous
- Computer ScienceProceedings 38th Annual Symposium on Foundations…
- 19 October 1997
It is proved that the class of languages recognizing by linear time, bounded error 2qfa's properly includes the regular languages, and 1-way and 2-way quantum finite state automata are introduced, which are the quantum analogues of deterministic, nondeterministic and probabilistic 1- way and2-way finite state Automata.
Quantum Arthur–Merlin games
It is proved that for one-message quantum Arthur–Merlin games, which correspond to the complexity class QMA, completeness and soundness errors can be reduced exponentially without increasing the length of Merlin’s message.
One-dimensional quantum walks
A quantum analog of the symmetric random walk, which the authors call the Hadamard walk, is analyzed, which has position that is nearly uniformly distributed in the range after steps, in sharp contrast to the classical random walk.
It is shown that fingerprints consisting of quantum information can be made exponentially smaller than the original strings without any correlations or entanglement between the parties, implying an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity.
Consequences and limits of nonlocal strategies
- R. Cleve, P. Høyer, B. Toner, J. Watrous
- MathematicsProceedings. 19th IEEE Annual Conference on…
- 12 April 2004
This paper investigates various aspects of the nonlocal effects that can arise when entangled quantum information is shared between two parties, and establishes limits on nonlocal behavior by upper-bounding the values of several of these games.
Parallelization, amplification, and exponential time simulation of quantum interactive proof systems
It is proved that any polynomial-round quan tum interactiveProof system with two-sided bounded error can be parallelized to a quantum interactive proof system with exponentially small one-sided error, in which the prover and verifier exchange only 3 messages.
Succinct quantum proofs for properties of finite groups
- J. Watrous
- Mathematics, Computer ScienceProceedings 41st Annual Symposium on Foundations…
- 7 September 2000
It is proved that for an arbitrary group oracle, there exist succinct (polynomial-length) quantum proofs for the Group Non-Membership problem that can be checked with small error in polynomial time on a quantum computer.
Two-way finite automata with quantum and classical state
Space-Bounded Quantum Complexity
- J. Watrous
- Computer ScienceJ. Comput. Syst. Sci.
- 1 October 1999
It is shown that unbounded error, space O(s) bounded quantum Turing machines and probabilistic Turing machines are equivalent in power and, furthermore, that any QTM running in space s can be simulated deterministically in NC2(2s)?DSPACE(s2)?DTIME(2O(s).