# How to multiply two vectors (kets) in qiskit?

Hi does anyone know how i could write a program to get the product of something like |1>|0>|0>?

• Do you mean the tensor product? This can be done as you can use the "statevector simulator". The qubits can be prepared to the desired state $|\psi\rangle$. Then the total output statevector may be the desired output
– 刘环宇
Nov 10 at 2:14
• What sort of multiplication do you have in mind? Tensor product? Inner product? Outer product? Nov 10 at 2:21

## Create computational basis state circuit

With qiskit, you can do it like this:

from qiskit.circuit  import QuantumCircuit
def create_computational_basis_state(basis_state: str):
qc = QuantumCircuit(len(basis_state))
for i, bit in enumerate(basis_state):
if int(bit) == 1: qc.x(i)
print(qc)
return qc


So for example:

qc = create_computational_basis_state('101')

┌───┐
q_0: ┤ X ├
└───┘
q_1: ─────
┌───┐
q_2: ┤ X ├
└───┘


## Extract the state vector

And if you want to get the vector/array of this state (the vector resulting from the tensor product) you can do the following:

from qiskit import Aer, execute
from qiskit.quantum_info import Statevector
backend = Aer.get_backend("statevector_simulator")
result = execute(qc, backend=backend, shots=1).result()
print('State Vector:', result.get_statevector() )

State Vector: [0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j]


In Qiskit you can easily do tensor product of two states using ^ operator as follows:

from qiskit.quantum_info import Statevector

state1 = Statevector.from_label('++')
state2 = Statevector.from_label('--')

# Tensor product:
tensored_state = state1 ^ state2

# Or equivalently:
tensored_state = state1.tensor(state2)

# Print the result:
from qiskit.visualization import array_to_latex
array_to_latex(tensored_state, max_size = 16)