Class Description

BQP/poly: BQP With Polynomial-Size Karp-Lipton Advice

Is to BQP/mpoly as ∃BPP is to MA. Namely, the BQP machine is required to give some answer with probability at least 2/3 even if the advice is bad. Even though BQP/mpoly is a more natural class, BQP/poly follows the standard definition of advice as a class operator [KL82].

Contained in BQP/mpoly and contains BQP/log.

Linked From

BPP/log: BPP With Logarithmic Karp-Lipton Advice

The class of problems solvable by a semantic BPP machine with O(log n) advice bits that depend only on the input length n. If the advice is good, the output must be correct with probability at least 2/3. If it is bad, the machine must provide some answer with probability at least 2/3. See the discussion for BQP/poly.

Contained in BPP/mlog.

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BQP/log: BQP With Logarithmic-Size Karp-Lipton Advice

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

Contained in BQP/mlog.

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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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