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.
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¶
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.