Matches in SemOpenAlex for { <https://semopenalex.org/work/W1905352783> ?p ?o ?g. }
- W1905352783 abstract "We propose a framework to study models of computation of indeterministic data, represented by abstract distributions. In these distributions, probabilities are replaced by amplitudes drawn from a fixed semi-ring $S$, of which the non-negative reals, the complex numbers, finite fields $mathbb F_{p^r}$, and cyclic rings $mathbb Z_k$ are examples. Varying $S$ yields different models of computation, which we may investigate to better understand the (likely) difference in power between randomised and quantum computation. The modal quantum states of Schumacher and Westmoreland [arXiv:1010.2929] are examples of such distributions, for $S$ a finite field. For $S = mathbb F_2$, Willcock and Sabry [arXiv:1102.3587] show that UNIQUE-SAT is solvable by polynomial-time uniform circuit families consisting of invertible gates. We characterize the decision problems solvable by polynomial uniform circuit families, using either invertible or unitary transformations over cyclic rings $S = mathbb Z_k$, or (in the case that $k$ is a prime power) finite fields $S = mathbb F_k$. In particular, for $k$ a prime power, these are precisely the problems in the class $mathsf{Mod}_kmathsf P$." @default.
- W1905352783 created "2016-06-24" @default.
- W1905352783 creator A5019353647 @default.
- W1905352783 date "2014-05-28" @default.
- W1905352783 modified "2023-09-27" @default.
- W1905352783 title "On computation with 'probabilities' modulo k" @default.
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