Almost-Everywhere Superiority for Quantum Polynomial-Time Languages

We prove that, relative to some black box, there are languages for which polynomial-time quantum machines are exponentially faster than each classical machine almost everywhere.

[1]  Patrick Billingsley,et al.  Probability and Measure. , 1986 .

[2]  Michael J. Fischer,et al.  Separating Nondeterministic Time Complexity Classes , 1978, JACM.

[3]  Alan L. Selman,et al.  A Hierarchy Theorem for Almost Everywhere Complex Sets With Application to Polynomial Complexity Degrees , 1987, Symposium on Theoretical Aspects of Computer Science.

[4]  Joel I. Seiferas,et al.  A Note on Almost-Everywhere-Complex Sets and Separating Deterministic-Time-Complexity Classes , 1991, Inf. Comput..

[5]  Jack H. Lutz.  Almost Everywhere High Nonuniform Complexity , 1992, J. Comput. Syst. Sci..

[6]  Eric Allender,et al.  Almost-Everywhere Complexity Hierarchies for Nondeterministic Time , 1993, Theor. Comput. Sci..

[7]  Gilles Brassard,et al.  Oracle Quantum Computing , 1994 .

[8]  Gilles Brassard,et al.  An exact quantum polynomial-time algorithm for Simon's problem , 1997, Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems.

[9]  Stephen A. Cook.  A Hierarchy for Nondeterministic Time Complexity , 1973, J. Comput. Syst. Sci..

[10]  Edith Hemaspaandra,et al.  Almost-Everywhere Superiority for Quantum Polynomial Time , 2002, Inf. Comput..

[11]  John Gill,et al.  Relative to a Random Oracle A, PA != NPA != co-NPA with Probability 1 , 1981, SIAM J. Comput..

[12]  Stanislav Zák,et al.  A Turing Machine Time Hierarchy , 1983, Theor. Comput. Sci..

[13]  Uwe Schöning,et al.  Complexity and Structure , 1986, Lecture Notes in Computer Science.