A new sibling of BQP
  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. 
Tereza Tusarova