A Generalized Floating-Point Representation and Manipulation of Quantum Signals Based on IEEE-754

Quantum information processing has become increasingly attractive in the past few decades due to its extraordinary performance. However, few results of quantum signal and its related manipulations based on quantum computation have emerged in recent years. The paper proposes a generalized floating-point representation of quantum signals (GFPRQS), which is improved by represent an arbitrary quantum signal with p + q qubits. In a floating-point representation, although every number is approximated using three registers, this format allows to represent a much larger range of values with a given number of qubits than a fixed-pointing representation. Based on GFPRQS representation, we first present the quantum circuits to accomplish basic signal modules (i.e., multiplyby 2 module, halving module, comparator module, swap module, etc,). And then, we design a composite module (i.e., sort module). At the end of the paper, to indicate the usability of the model GFPRQS an example involving the mean filtering and its quantum circuit is given.