QMA ⊆ PP

QMA is contained in PP.

Statement

Migrated verbatim from quantum-classical-merlin-arthur § Known relationships:

• $\mathbf{QCMA}\subseteq \mathbf{PP}\subseteq \mathbf{PSPACE}$, since $\mathbf{QMA}\subseteq \mathbf{PP}$.

Migrated verbatim from quantum-merlin-arthur § Known relationships:

• $\mathbf{QMA}\subseteq \mathbf{PP}\subseteq \mathbf{PSPACE}$: QMA is contained in PP (Marriott-Watrous — TODO citation), and thus in PSPACE.

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

class: free because a containment between complexity classes is proved by any argument at all; the reduction-class axis does not discriminate here, and unstated would wrongly suggest the information is missing.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• MISSING CITATION (Marriott-Watrous / Kitaev-Watrous); the same fact is a ‘TODO citation’ at quantum-merlin-arthur.md:29.
• It appears on the page only as a trailing ‘since’ clause, not as a claim in its own right.
• Uncited: the bullet says ‘Marriott-Watrous — TODO citation’ and no reference page exists (the containment is Kitaev-Watrous 2000, strengthened by Marriott-Watrous 2005).
• PP is not wikilinked on the bullet although content/Complexity/probabilistic-polynomial-time.md exists.
• Duplicates the same containment stated at content/Complexity/quantum-classical-merlin-arthur.md:25.