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Subtraction

Subtraction (denoted as ’-’) is implemented by negation and addition in 2-complement representation. a−b⟷a+(−b)⟷a+∼b+lsb_valuea - b \longleftrightarrow a + (-b) \longleftrightarrow a + \sim{b} + lsb\_value Where ’~’ is bitwise not and lsb_valuelsb\_value is the least significant bit value. Note that integer and fixed-point numbers are represented in a 2-complement method during function evaluation. The binary number is extended in the case of a register size miss-match. For example, the positive signed number (110)2=6(110)_2=6 is expressed as (00110)2(00110)_2 when operating with a 5-qubit register. Similarly, the negative signed number (110)2=−2(110)_2=-2 is expressed as (11110)2(11110)_2. Examples: 5 + 3 = 8 , 0101 + 0011 = 1000 5 - 3 = 5 + (-3) = 2, 0101 + 1101 = 0010 -5 + -3 = -8, 1011 + 1101 = 1000

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Examples

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Example 1: Subtraction of Two Quantum Variables

This example generates a quantum program that subtracts one quantum variables from the other, both of size 3 qubits. 
from classiq import *


@qfunc
def main(a: Output[QNum], b: Output[QNum], res: Output[QNum]) -> None:
    a |= 4
    b |= 5
    res |= a - b


qmod = create_model(main)


qprog = synthesize(qmod)

result = execute(qprog).result_value()
print(result.parsed_counts)
Output:
[{'a': 4.0, 'b': 5.0, 'res': -1.0}: 1000]

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Example 2: Subtraction of a Float from a Register

This example generates a quantum program which subtracts two argument. The left_arg is defined to be a fix point number (11.1)2(11.1)_2 (3.5). The right_arg is defined to be a quantum register of size of three. 
@qfunc
def main(a: Output[QNum], res: Output[QNum]) -> None:
    a |= 4
    res |= a - 3.5


qmod = create_model(main)


qprog = synthesize(qmod)

result = execute(qprog).result_value()
print(result.parsed_counts)
Output:
[{'a': 4.0, 'res': 0.5}: 1000]