# Comparators¶

The following comparators are supported:

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

{
"function": "Equal",
"function_params": {
"left_arg": 3,
"right_arg": {
"size": 3
}
}
}


### Register Names¶

By default, the input registers are called left_arg and right_arg. If the name field of a RegisterUserInput object is specified, then the name of the register is determined accordingly. If one of the arguments is a constant then it is not available as an input register.

The output registers include the result register. By default, its name is determined by the specific comparator used: is_equal, is_less_than, etc. It may be overridden by the output_name argument. In addition, the input registers are also available as output registers, with the same names.

### Example 1: Two Register¶

{
"logic_flow": [
{
"function": "Equal",
"function_params": {
"left_arg": {
"size": 5,
"is_signed": true
},
"right_arg": {
"size": 3
}
}
}
]
}

from classiq import ModelDesigner, QUInt, QSInt
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_designer = ModelDesigner()
model_designer.Equal(params)
circuit = model_designer.synthesize()


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¶

{
"logic_flow": [
{
"function": "Equal",
"function_params": {
"left_arg": 3,
"right_arg": {
"size": 3
}
}
}
]
}

from classiq import ModelDesigner
from classiq.builtin_functions import Equal
from classiq.interface.generator.arith.arithmetic import RegisterUserInput

params = Equal(left_arg=3, right_arg=RegisterUserInput(size=3))
model_designer = ModelDesigner()
model_designer.Equal(params)
circuit = model_designer.synthesize()


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.