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Subtraction

Subtraction (denoted as '-') is implemented by negation and addition in 2-complement representation.

\[ a - b \longleftrightarrow a + (-b) \longleftrightarrow a + \sim{b} + lsb \\_ value \]

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:

{
  "function": "Subtractor",
  "function_params": {
    "left_arg": 3,
    "right_arg": {
      "size": 3
    },
    "inplace": false
  }
}

Example 1: Two Register

{
        "constraints": {
          "max_width": 8,
          "max_depth": 40
        },
        "logic_flow": [
            {
                "function": "Subtractor",
                "function_params": {
                    "left_arg": {"size": 3},
                    "right_arg": {"size": 3}
                }
            }
        ]
    }

from classiq import ModelDesigner, 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_designer = ModelDesigner()
model_designer.Subtractor(params)
circuit = model_designer.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:

img_1.png

Example 2: Float and Register

{
    "constraints": {
      "max_width": 6,
      "max_depth": 40
    },
    "logic_flow": [
        {
            "function": "Subtractor",
            "function_params": {
                "left_arg": 3.5,
                "right_arg": {
                    "size": 3
                }
            }
        }
    ]
}

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

params = Subtractor(left_arg=3.5, right_arg=RegisterUserInput(size=3))
model_designer = ModelDesigner()
model_designer.Subtractor(params)
circuit = model_designer.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:

img.png