Interested in learning how to program quantum computers? Then check out our Qiskit textbook Introduction to Quantum Computing with Qiskit.

Introduction

In this tutorial we will see how to construct a quantum logic gate from a unitary matrix.

In quantum computing unitary matrices are very important as they describe how quantum logic gates and circuits affect qubit states.

In Qiskit a quantum logic gate can be created from a unitary matrix using the Unitary class:

Unitary(data)

Where:

data: This is the unitary matrix that will be encoded in to the logic gate

For example the Pauli X gate can be described using the following matrix:

Using the unitary class we can implement the Pauli-X gate like so:

circuit.unitary([[0,1],[1,0]],q[0])

Where [[0,1],[1,0]] is the matrix we wish to encode and q[0] is the target qubit.

Implementation

In this section we will go through the full implementation step by step. The matrix we will be implementing is the Pauli-X gate matrix.

Step 1: Import modules

from qiskit import QuantumRegister, ClassicalRegister
from qiskit import QuantumCircuit, execute
from qiskit.quantum_info.operators import Operator
from qiskit import Aer

Step 2: Initialise the Backend

The next step is to intialise the backend device. Since this is only a tutorial we will use the Aer unitary simulator:

backend = Aer.get_backend('aer_simulator')

Step 3: Create the circuit

The next step is to create the circuit. This is just a one qubit circuit that creates a Pauli-X gate using the unitary class. Then the qubit is measured.

q = QuantumRegister(1,'q')
c = ClassicalRegister(1,'c')

circuit = QuantumCircuit(q,c)

circuit.unitary([[0,1],[1,0]],q[0])
circuit.measure(q,c)

Step 4: Execute the circuit and obtain the results

job = execute(circuit, backend, shots=8192)

counts = job.result().get_counts()

print(counts)

Code

from qiskit import QuantumRegister, ClassicalRegister
from qiskit import QuantumCircuit, execute
from qiskit.quantum_info.operators import Operator
from qiskit import Aer

backend = Aer.get_backend('aer_simulator')

q = QuantumRegister(1,'q')
c = ClassicalRegister(1,'c')

circuit = QuantumCircuit(q,c)

circuit.unitary([[0,1],[1,0]],q[0])
circuit.measure(q,c)

print(circuit)

job = execute(circuit, backend, shots=8192)

counts = job.result().get_counts()

print(counts)

How to create a quantum gate from a unitary matrix in Qiskit with code