https://doi.org/10.1140/epjqt/s40507-024-00222-4
Research
Designs of the divider and special multiplier optimizing T and CNOT gates
1
College of Computer and Control Engineering, Minjiang University, 350108, Fuzhou, Fujian, China
2
College of Electronic and Information Engineering, Guangxi Normal University, 541004, Guilin, Guangxi, China
Received:
3
February
2024
Accepted:
14
February
2024
Published online:
23
February
2024
Quantum circuits for multiplication and division are necessary for scientific computing on quantum computers. Clifford + T circuits are widely used in fault-tolerant realizations. T gates are more expensive than other gates in Clifford + T circuits. But neglecting the cost of CNOT gates may lead to a significant underestimation. Moreover, the small number of qubits available in existing quantum devices is another constraint on quantum circuits. As a result, reducing T-count, T-depth, CNOT-count, CNOT-depth, and circuit width has become the important optimization goal. We use 3-bit Hermitian gates to design basic arithmetic operations. Then, we present a special multiplier and a divider using basic arithmetic operations, where ‘special’ means that one of the two operands of multiplication is non-zero. Next, we use new rules to optimize the Clifford + T circuits of the special multiplier and divider in terms of T-count, T-depth, CNOT-count, CNOT-depth, and circuit width. Comparative analysis shows that the proposed multiplier and divider have lower T-count, T-depth, CNOT-count, and CNOT-depth than the current works. For instance, the proposed 32-bit divider achieves improvement ratios of 40.41 percent, 31.64 percent, 45.27 percent, and 65.93 percent in terms of T-count, T-depth, CNOT-count, and CNOT-depth compared to the best current work. Further, the circuit widths of the proposed n-bit multiplier and divider are 3n. I.e., our multiplier and divider reach the minimum width of multipliers and dividers, keeping an operand unchanged.
Key words: Quantum multiplier / Quantum divider / Quantum arithmetic operators / Clifford + T circuits
© The Author(s) 2024
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