Class Description

BQP/qlog: BQP With Logarithmic-Size Quantum Advice

Same as BQP/mlog except that the advice is quantum instead of classical.

Strictly contains BQP/mlog [NY03].

Contained in BQP/mpoly.

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BQP/mlog: BQP With Logarithmic-Size Deterministic Merlin-Like Advice

Same as BQP/mpoly except that the advice is O(log n) bits instead of a polynomial number.

Strictly contained in BQP/qlog [NY03].

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BQP/mpoly: BQP With Polynomial-Size Deterministic Merlin-Like Advice

The class of languages recognized by a syntactic BQP machine with deterministic polynomial advice that depends only on the input length, such that the output is correct with probability 2/3 when the advice is good.

Can also be defined as the class of problems solvable by a nonuniform family of polynomial-size quantum circuits, just as P/poly is the class solvable by a nonuniform family of polynomial-size classical circuits.

Referred to with a variety of other ad hoc names, including BQP/poly on occassion.

Contains BQP/qlog, and is contained in BQP/qpoly.

Does not contain ESPACE [NY03].

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