# Table 1 Resources for the elementary gates. We here assume that operands are n-bit. We omit subleading terms with respect to n

Gate Logical qubits T-count Reference
Total Operand Output Ancilla
Adder 2n 2n 0 (self-update) 0 14n [37, 38, 46]
Ctrl Adder 2n 2n 0 (self-update) 0 21n [42, 46]
Modular Adder 2n 2n 0 (self-update) 0 70n [26, 37, 38, 46]
Multiplier 3n 2n n 0 $$21n^{2}$$ [42]
Divider 5n 2n n 2n $$35n^{2}$$ [46]
Multi Ctrl Toffoli 2n n 1 n 8n [18, 48]
Square Root 4n n n 2n $$14n^{2}$$ [52]
arccos 105     3.4 × 104 [51]
controlled rotation (with accuracy of $$2^{-n}$$) 2     3n [16, 47, 53]
1. Since the modular adder is constructed by 5 plain adders [26], its T-count is 5 times the values of the adder.
2. The circuit given in [52] takes an n-bit input and returns an n/2-bit output of square root and an n/2-bit remainder. To keep n-bit accuracy, we add n qubits with 0’s to the input of the circuit and calculate the n-bit square root with 2n-bit input. The added n bits are treated as the input, and the n bits remainder is treated as ancillae.