  We define the problem identity check: Given a classical description of a
quantum circuit, determine whether it is almost equivalent to the identity.
Explicitly, the task is to decide whether the corresponding unitary is close to
a complex multiple of the identity matrix with respect to the operator norm. We
show that this problem is QMA-complete.
  A generalization of this problem is equivalence check: Given two descriptions
of quantum circuits and a description of a common invariant subspace, decide
whether the restrictions of the circuits to this subspace almost coincide. We
show that equivalence check is also in QMA and hence QMA-complete.
