# Comparators¶

The following comparators are supported:

• Equal (denoted as '==')
• NotEqual (denoted as '!=')
• GreaterThan (denoted as '>')
• GreaterEqual (denoted as '>=')
• LessThan (denoted as '<')
• LessEqual (denoted as '<=')

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 $$(110)_2=6$$ is expressed as $$(00110)_2$$ when operating with a 5-qubit register. Similarly, the negative signed number $$(110)_2=-2$$ is expressed as $$(11110)_2$$.

Examples:

(5 <= 3) = 0

(5 == 5) = 1

($$(011)_2$$ == $$(11)_2$$) = 1

(signed $$(101)_2$$ < unsigned $$(101)_2$$) = 1

## Syntax¶

Function: Equal/NotEqual/GreaterThan/GreaterEqual/LessThan/LessEqual

Parameters:

• left_arg: Union[float, int, RegisterUserInput] (see RegisterUserInput)
• right_arg: Union[float, int, RegisterUserInput] (see RegisterUserInput)
• output_size: Optional[PositiveInt]

Register names:

• left_arg: left_arg
• right_arg: right_arg
• result: is_equal/ is_not_equal/ is_greater_than/ is_greater_equal/ is_less_than/ is_less_equal, respectively.
{
"function": "Equal",
"function_params": {
"left_arg": 3,
"right_arg": { "size": 3 }
}
}


### Example 1: Two Register¶

{
"functions": [
{
"name": "main",
"body": [
{
"function": "Equal",
"function_params": {
"left_arg": {
"size": 5,
"is_signed": true
},
"right_arg": {
"size": 3
}
}
}
]
}
]
}

from classiq import Model, QUInt, QSInt, synthesize
from classiq.builtin_functions import Equal

params = Equal(
left_arg=QSInt(size=5).to_register_user_input(),
right_arg=QUInt(size=3).to_register_user_input(),
)
model = Model()
model.Equal(params)
quantum_program = synthesize(model.get_model())


This example generates a circuit that performs 'equal' between two registers. The left arg is a signed register with 5 qubits and the right arg is an unsigned register with 3 qubits. ### Example 2: Integer and Register¶

{
"functions": [
{
"name": "main",
"body": [
{
"function": "Equal",
"function_params": {
"left_arg": 3,
"right_arg": {
"size": 3
}
}
}
]
}
]
}

from classiq import Model, RegisterUserInput, synthesize
from classiq.builtin_functions import Equal

params = Equal(left_arg=3, right_arg=RegisterUserInput(size=3))
model = Model()
model.Equal(params)
quantum_program = synthesize(model.get_model())


This example generates a circuit that performs 'equal' between a quantum register and an integer. The left arg is an integer equal to three and the right arg is an unsigned quantum register with 3 qubits. 