Introductino to Quantum Computing with Qiskit

Section 5.1 Introductino to Quantum Computing with Qiskit

Note ID: 202604120001 | Tags: <tensor products>, <Qiskit>, <state vectors>

Exercises Problem Set 1

Imports.

from quiskit.quantum_info import Statevector, Operator
import numpy as np
from numpy import sqrt
from IPython.display import display, Latex, Math

from qiskit import __version__
print(f"Qiskit version: {__version__}")

Tensor Products.

1.

Use Qiskit to compute the tensor product \(\ket{-} \otimes \ket{i}\text{.}\) Your solution must construct the state and print out the amplitudes in the computational basis.

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Hint.

Use

Statevector.from_label("-") for \(\ket{-}\)

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Statevector.from_label("r") for \(\ket{i}\)

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Answer.

\(\frac{1}{2} \ket{00} + \frac{i}{2} \ket{01} - \frac{1}{2} \ket{10} - \frac{i}{2} \ket{11}\)

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Solution.

# Declare state vectors
minus = Statevector.from_label("-")
plus_i = Statevector.from_label("r")

# Compute the tensor product and display the result
display(minus.tensor(plus_i).draw("latex"))

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2.

Given the state \(\ket{0} \otimes \ket{1} \otimes \ket{+}\) write the state vector ordering explicitly.

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Hint.

🎗️ Quiskit starts its indexing (qubit 0) from the right-hand side.

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Answer.

\(\frac{\sqrt{2}}{2}\ket{010} + \frac{\sqrt{2}}{2}\ket{011}\)

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Solution.

zero = Statevector([1, 0])
one = Statevector([0, 1])
plus = Statevector.from_label("+")

display((zero ^ one ^ plus).draw("latex"))

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