Abstract
Quantum modular multiplication circuit is one of the basic quantum computation circuits which are basic functions in quantum algorithms. However, since quantum-quantum modular multipliers require a high cost reversible modular inversion routine for modular multiplication, researchers have been unable to propose a feasible quantum-quantum modular multiplier. In this paper, we proposed efficient quantum-classical modular multipliers and the first quantum-quantum modular multipliers that do not require a reduction stage by transforming the partial product used in multiplication utilizing bit-shift operation. Then, we calculated quantum resource complexity and analyzed it compared to other quantum modular multipliers and utilized ETRI (Electronics and Telecommunications Research Institute) Qcrypton to analyze quantum resource complexity in the practical quantum computing situation. The proposed quantum modular multipliers show an improvement of 50% in terms of gates and circuit depth compared to the most recently proposed high-performance quantum modular multipliers.
Highlights
I N 1981, Richard Feynman proposed a quantum computer utilizing quantum superposition
While the classical computers use the bit with a value of 0 or 1 as the elementary unit of information, the quantum computer uses the qubit in which the state of 0 and 1 exists simultaneously as a probabilistic superposition state
Due to this superposition state, quantum computers can express the data in a high dimensional form, and even a small number of qubits can simultaneously represent a large number of cases
Summary
I N 1981, Richard Feynman proposed a quantum computer utilizing quantum superposition. In 1994, Peter Shor proposed the Shor algorithm to solve the problem of factoring and discrete logarithm within a polynomial time [3], [4] These quantum algorithms use a large number of quantum computation circuits. We use a bit shift and bit circulation method that transforms the form of partial product in the multiplication process for efficient quantum modular multiplication instead of the reduction stage. Using these methods, we propose quantum-classical and quantumquantum modular multipliers, reducing the multiplier complexity. To eliminate the reduction stage, we proposed the quantum modular multiplication circuits which proceed multiplication using the method of transforming the partial product using bit shift operation. We utilized the ETRI Qcrypton to analyze the complexity of quantum resources in the practical quantum computing situation
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