Addition¶
The "Addition" operation, denoted '+', is implemented according to the following truth table. Here \(a\) and \(b\) denote numbers, \(i\) bit index, and \(c_{in / out}\) the incoming and outgoing carries of that step, respectively.
\(a_i\) | \(b_i\) | \(c_{in}\) | \({(a + b)}_i\) | \(c_{out}\) |
---|---|---|---|---|
0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 1 |
0 | 0 | 1 | 1 | 0 |
0 | 1 | 1 | 0 | 1 |
1 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 |
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 = 2, 0101 + 1101 = 0010
- -5 + -3 = -8, 1011 + 1101 = 1000
Several adder algorithms, differing in depth, number of gates used, and number of auxiliaries, are implemented [1][2].
Syntax¶
Function: Adder
Parameters:
left_arg
: Union[float, int, FixPointNumber, RegisterUserInput]right_arg
: Union[float, int, FixPointNumber, RegisterUserInput]output_size
: Optional[PositiveInt]output_name
: Optional[str]inplace
: bool = True
{
"function": "Adder",
"function_params": {
"left_arg": 3,
"right_arg": {
"size": 3
},
"inplace": false
}
}
Example 1: Two Register Addition¶
{
"constraints": {
"max_width": 7,
"max_depth": 100
},
"logic_flow": [
{
"function": "Adder",
"function_params": {
"left_arg": {"size": 3},
"right_arg": {"size": 3}
}
}
]
}
from classiq import ModelDesigner
from classiq.builtin_functions import Adder
from classiq.interface.generator.arith.arithmetic import RegisterUserInput
params = Adder(left_arg=RegisterUserInput(size=3), right_arg=RegisterUserInput(size=3))
model_designer = ModelDesigner()
model_designer.Adder(params)
circuit = model_designer.synthesize()
This code example generates a circuit that adds 2 arguments. Both "left_arg" and "right_arg" are defined to be quantum registers of size 3.
Generated Circuit¶
Example 2: Float and Register Addition¶
{
"constraints": {
"max_width": 5,
"max_depth": 100
},
"logic_flow": [
{
"function": "Adder",
"function_params": {
"left_arg": 3.5,
"right_arg": {
"size": 3
}
}
}
]
}
from classiq import ModelDesigner
from classiq.builtin_functions import Adder
from classiq.interface.generator.arith.arithmetic import RegisterUserInput
params = Adder(left_arg=3.5, right_arg=RegisterUserInput(size=3))
model_designer = ModelDesigner()
model_designer.Adder(params)
circuit = model_designer.synthesize()
This code example generates a circuit that adds 2 arguments. Here "left_arg" is a fixed-point number \((11.1)_2\) and "right_arg" a quantum register of size 3.
Generated Circuit¶
References¶
[1]S. A. Cuccaro, T. G. Draper, S. A. Kutin, and D. P. Moulton, “A new quantum ripple-carry addition circuit,” arXiv:quant-ph/0410184, Oct. 2004, Accessed: Aug. 09, 2021. [Online]. Available: http://arxiv.org/abs/quant-ph/0410184
[2]T. G. Draper, “Addition on a Quantum Computer,” arXiv:quant-ph/0008033, Aug. 2000, Accessed: Aug. 09, 2021. [Online]. Available: http://arxiv.org/abs/quant-ph/0008033