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Multiplication

The multiplication operation, denoted '\(*\)', is a series of additions ("long multiplication"). The multiplier has different implementations, depending on the type of adder in use.

Note that integer and fixed-point numbers are represented in a two-complement method during function evaluation. The binary number is extended in the case of a register size mismatch. For example, the positive signed number \((110)_2=6\) is expressed as \((00110)_2\) when working with a five-qubit register. Similarly, the negative signed number \((110)_2=-2\) is expressed as \((11110)_2\).

Examples

The calculation of -5 * 3 = -15.

The left arg -5 is represented as 1011 and 3 as 11. The number of digits needed to store the answer is 4+2-1 = 5. The multiplication is done in the 'regular' manner where each number is extended to five bits and only five digits are kept in the intermediary results.

\[ \begin{equation*}\begin{array}{c} \phantom{\times}11011\\ \underline{\times\phantom{000}11}\\ \phantom{\times}11011\\ \underline{\phantom\times1011\phantom9}\\ \phantom\times10001 \end{array}\end{equation*} \]

Syntax

Function: Multiplier

Parameters:

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

Register names:

  • left_arg: left_arg
  • right_arg: right_arg
  • result: product
{
  "function": "Multiplier",
  "function_params": {
    "left_arg": 3,
    "right_arg": { "size": 3 }
  }
}

Example 1: Two-Register Multiplication

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

from classiq import Model, QUInt, synthesize, show
from classiq.builtin_functions import Multiplier

params = Multiplier(
    left_arg=QUInt(size=3).to_register_user_input(),
    right_arg=QUInt(size=3).to_register_user_input(),
)
model = Model()
model.Multiplier(params)
quantum_program = synthesize(model.get_model())
show(quantum_program)

This code example generates a circuit that multiplies two arguments. Both left_arg and right_arg are defined as quantum registers of size three.

Generated Circuit

img.png

Example 2: Float and Register Multiplication

{
  "functions": [
    {
      "name": "main",
      "body": [
          {
            "function": "Multiplier",
            "function_params": {
                "left_arg": 3.5,
                "right_arg": {
                    "size": 3
                }
            }
          }
      ]
    }
  ]
}

from classiq import Model, RegisterUserInput, synthesize, show
from classiq.builtin_functions import Multiplier

params = Multiplier(left_arg=3.5, right_arg=RegisterUserInput(size=3))
model = Model()
model.Multiplier(params)
quantum_program = synthesize(model.get_model())
show(quantum_program)

This code example generates a circuit that multiplies two arguments. Here, left_arg is a fixed-point number \((11.1)_2\) and right_arg is a quantum register of size three.

Generated Circuit

img.png