  In this article, we propose a general principle of quantum interference for
quantum system, and based on this we propose a new type of computing machine,
the duality computer, that may outperform in principle both classical computer
and the quantum computer.
  According to the general principle of quantum interference, the very essence
of quantum interference is the interference of the sub-waves of the quantum
system itself. A quantum system considered here can be any quantum system: a
single microscopic particle, a composite quantum system such as an atom or a
molecule, or a loose collection of a few quantum objects such as two
independent photons.
  In the duality computer, the wave of the duality computer is split into
several sub-waves and they pass through different routes, where different
computing gate operations are performed. These sub-waves are then re-combined
to interfere to give the computational results. The quantum computer, however,
has only used the particle nature of quantum object. In a duality computer, it
may be possible to find a marked item from an unsorted database using only a
single query, and all NP-complete problems may have polynomial algorithms. Two
proof-of-the-principle designs of the duality computer are presented: the giant
molecule scheme and the nonlinear quantum optics scheme. We also proposed
thought experiment to check the related fundamental issues, the measurement
efficiency of a partial wave function
