Multiplication

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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 = - 1

The left arg -5 is represented as 1011 and 3 as

The number of digits needed to store the answer is 4+2-1 =
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{array}{c} \phantom{\times}11011\\ \underline{\times\phantom{000}11}\\ \phantom{\times}11011\\ \underline{\phantom\times1011\phantom9}\\ \phantom\times10001 \end{array}

Examples

Example 1: Two Quantum Variables Multiplication

This code example generates a quantum program that multiplies two arguments. Both of them are defined as quantum variables of size

from classiq import *


@qfunc
def main(a: Output[QNum], b: Output[QNum], res: Output[QNum]) -> None:
    a |= 4
    b |= 5
    res |= a * b

qprog = synthesize(main)

result = sample(qprog)
result

Output:

Submitting job to simulator
  Job: https://platform.classiq.io/jobs/fd80ef81-6bcd-4abd-869f-fbd7bd5aec80
  

	a	b	res	counts	probability	bitstring
0	4	5	20	2048	1.0	10100101100

Example 2: Float and Quantum Variable Multiplication

This code example generates a quantum program that multiplies two arguments. Here, the left argument is a fixed-point number

(11.1)_2

(3.5), and the right argument is a quantum variable of size

@qfunc
def main(a: Output[QNum], res: Output[QNum]) -> None:
    allocate(2, a)

    hadamard_transform(a)
    res |= 3.5 * a

qprog = synthesize(main)

result = sample(qprog)
result

Output:

Submitting job to simulator
  Job: https://platform.classiq.io/jobs/fca22608-e8f9-4465-9942-aca0056ca6ff
  

	a	res	counts	probability	bitstring
0	0	0.0	527	0.257324	0000000
1	3	10.5	512	0.250000	1010111
2	2	7.0	507	0.247559	0111010
3	1	3.5	502	0.245117	0011101

Algorithms

Applications

Tutorials

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Examples

Examples

Example 1: Two Quantum Variables Multiplication

Example 2: Float and Quantum Variable Multiplication

View on GitHub

​Examples

​Examples

​

​Example 1: Two Quantum Variables Multiplication

​

​Example 2: Float and Quantum Variable Multiplication

Examples

Examples

Example 1: Two Quantum Variables Multiplication

Example 2: Float and Quantum Variable Multiplication