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Quantum computing and quadratically signed weight enumerators. (English) Zbl 1032.68080
Summary: We prove that quantum computing is polynomially equivalent to classical probabilistic computing with an oracle for estimating the value of simple sums, quadratically signed weight enumerators (QWGTs). The problem of estimating these sums is cast in terms of promise problems and has two interesting variants. An oracle for the unconstrained variant may be more powerful than quantum computing, while an oracle for a more constrained variant is efficiently solvable in the one-bit model of quantum computing. Thus, problems involving QWGTs yield new problems in BQPP (BQP promise problems) and a natural BQPP complete problem. They can be used to define and study complexity classes and their relationships to quantum computing.

MSC:
68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
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