Two
QCMA-complete problems
(pp635-643)
Pawel
Wocjan,
Dominik
Janzing,
and
Thomas
Beth
doi:
https://doi.org/10.26421/QIC3.6-7
Abstracts:
QMA and QCMA are possible quantum analogues of the
complexity class NP. In QMA the proof is a quantum state and the
verification is a quantum circuit. In contrast, in QCMA the proof is
restricted to be a classical state. It is not known whether QMA strictly
contains QCMA. Here we show that two known QMA-complete problems can be
modified to QCMA-complete problems in a natural way: (1) Deciding
whether a 3-local Hamiltonian has low energy states (with energy smaller
than a given value) that can be prepared with at most k elementary
gates is QCMA-complete, whereas it is QMA-complete when the restriction
on the complexity of preparation is dropped. (2) Deciding whether a
(classically described) quantum circuit does not act as the identity on all
basis states is
QCMA-complete. It is QMA-complete to decide whether it does not act on all
states as
the identity.
Key words: quantum
complexity, quantum NP, QCMA, quantum circuit design |