Quantum Logic Implementation of Unary Arithmetic Operations

The mathematical property of inheritance for certain unary fixed point operations has recently been exploited to enable the efficient formulation of arithmetic algorithms and circuits for operations such as the modular multiplicative inverse, exponentiation, and discrete logarithm computation in classical binary logic circuits. This principle has desirable features with regard to quantum logic circuit implementations and is generalized for the case of MVL arithmetic systems. It is shown that the inheritance principle in conjunction with the bijective nature of many unary functions is used to realize compact quantum logic cascades that require no ancilla digits and generate no garbage outputs.