Abstract
The implementation of quantum computing processors for scientific applications includes quantum floating points circuits for arithmetic operations. This work adopts the standard division algorithms for floating-point numbers with restoring, non-restoring, and Goldschmidt division algorithms for single-precision inputs. The design proposals are carried out while using the quantum Clifford+T gates set, and resource estimates in terms of numbers of qubits, T-count, and T-depth are provided for the proposed circuits. By improving the leading zero detector (LZD) unit structure, the proposed division circuits show a significant reduction in the T-count when compared to the existing works on floating-point division.
Highlights
IntroductionCircuits can be designed using the fault-tolerant Clifford+T gates set to overcome the noise-intolerant behavior of physical quantum computing systems
Quantum integer circuits attracted researchers to implement Shor’s factorization algorithm, in order to address fundamental arithmetic problems on a quantum computer and resolve discrete logarithmic problems in a polynomial time [1]
Quantum computers simulate some problems with large-scale qubits that are not available, yet that are essential in constructing some optimum quantum circuits to assist in the efficient hardware design of future quantum computers [5]
Summary
Circuits can be designed using the fault-tolerant Clifford+T gates set to overcome the noise-intolerant behavior of physical quantum computing systems. QFT circuits utilize fault-tolerant T gate to propose a fault-tolerant phase rotations, which presents an additional overhead on T-count or ancillary qubits [18,20]. A quantum division circuit for single-precision floating-point (SPFP) number is proposed using restoring, non-restoring, and Goldschmidt algorithms. The critical goal in developing a quantum division circuit using Restoring, non-restoring, and Goldschmidt algorithm is to minimize the T-count and T-depth of the proposed quantum circuit.
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