Subtraction¶
Subtraction (denoted as '-') is implemented by negation and addition in 2-complement representation.
Where '~' is bitwise not and lsb_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 \((110)_2=6\) 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 = 8 , 0101 + 0011 = 1000
5 - 3 = 5 + (-3) = 2, 0101 + 1101 = 0010
-5 + -3 = -8, 1011 + 1101 = 1000
Syntax¶
Function: Subtractor
Parameters:
left_arg
: Union[float, int, FixPointNumber, RegisterUserInput]right_arg
: Union[float, int, FixPointNumber, RegisterUserInput]output_size
: Optional[PositiveInt]output_name
: Optional[str]inplace_arg
: Optional[str] = None
{
"function": "Subtractor",
"function_params": {
"left_arg": 3,
"right_arg": {
"size": 3
},
"inplace_arg": null
}
}
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, it is called difference
,
but its name may be overridden by the output_name
argument.
The inplace_arg
argument sets the argument to override.
If it is set to None
, the input registers are also available as output registers, with the
same names. If it is set to left
or right
, only the right or left argument will be available, respectively.
The qubits of the overriden argument will be used for the result.
Example 1: Two Register¶
{
"logic_flow": [
{
"function": "Subtractor",
"function_params": {
"left_arg": {"size": 3},
"right_arg": {"size": 3}
}
}
]
}
from classiq import Model, QUInt
from classiq.builtin_functions import Subtractor
params = Subtractor(
left_arg=QUInt(size=3).to_register_user_input(),
right_arg=QUInt(size=3).to_register_user_input(),
)
model = Model()
model.Subtractor(params)
circuit = model.synthesize()
This example generates a circuit which subtracts two arguments. The left_arg is defined to be a quantum register of size three. The right_arg is defined to be a quantum register of size three.
Output circuit:
Example 2: Float and Register¶
{
"logic_flow": [
{
"function": "Subtractor",
"function_params": {
"left_arg": 3.5,
"right_arg": {
"size": 3
}
}
}
]
}
from classiq import Model, RegisterUserInput
from classiq.builtin_functions import Subtractor
params = Subtractor(left_arg=3.5, right_arg=RegisterUserInput(size=3))
model = Model()
model.Subtractor(params)
circuit = model.synthesize()
This example generates a circuit which subtracts two argument. The left_arg is defined to be a fix point number \((11.1)_2\). The right_arg is defined to be a quantum register of size of three.
Output circuit: