  We present a new quantum complexity class, called MQ^2, which is contained in
AWPP. This class has a compact and simple mathematical definition, involving
only polynomial-time computable functions and a unitarity condition. It
contains both Deutsch-Jozsa's and Shor's algorithm, while its relation to BQP
is unknown. This shows that in the complexity class hierarchy, BQP is not an
extraordinary isolated island, but has ''siblings'' which as well can solve
prime-factorization.
