Allowable Generalized Quantum Gates

In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form Σ d- 1 i = 0 p i U i , and the p i 's are complex numbers with module less or equal to 1 and constrained by |Σ i p i |≤1.