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Introduction

In this tutorial we will explore the U gate and how to implement it in Qiskit on IBM Quantum Computers.

What is the U gate?

The U gate is a gate that does a rotation around the Bloch sphere with 3 Euler angles. The three angles used to perform the rotations are θ,λ, and φ.

The operation of the U can be described with the following matrix:

The U gate can replicate any other single qubit gate. For example to replicate the Pauli-X gate you would rotate θ by π, φ by π and λ by π/2 :

Where U(π, π, π/2 ) = U(θ, φ, λ)

As an example lets replicate a Pauli-X gate and set the qubit state to |1〉To see how the U gate operates on the qubit we multiply the column vector associated with |1〉by the U gate matrix.

This is correct as the resulting column vector is for |0〉This shows that the qubits state has flipped from |1〉to |0〉

If we wanted to use a U gate to create a Hadamard gate then the parameters would be set like so:

Let’s prove this by setting the qubit to |0〉 and then by multiplying the state vector by the U gate matrix with the parameters set as above:

Which has put the qubit in to superposition just as the Hadamard gate would!

Implementation

In Qiskit the U gate can be implemented very easily with the following line of code:

circuit.u(theta, phi, lam,q[0])

Where theta, phi, and lam are the 3 Euler angles and q[0] is the qubit that the U gate is applied to.

For example lets say we want to replicate a Pauli-X gate using the U gate. We will need to set theta and phi to π and lambda to π/2 like so:

circuit.u(pi, pi, pi/2,q[0])

How to run the program

Copy and paste the code below in to a python file

Enter your API token in the IBMQ.enable_account('Insert API token here') part
Save and run

Code

from qiskit import QuantumRegister, ClassicalRegister
from qiskit import QuantumCircuit, execute,IBMQ
from qiskit.tools.monitor import job_monitor
import numpy

pi = numpy.pi

IBMQ.enable_account('ENTER API KEY HERE')
provider = IBMQ.get_provider(hub='ibm-q')

backend = provider.get_backend('ibmq_qasm_simulator')

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


circuit = QuantumCircuit(q,c)

circuit.u(pi,pi,pi/2,q[0]) # U3 Gate
circuit.measure(q,c) # Qubit Measurment

print(circuit)

job = execute(circuit, backend, shots=8192)
    
job_monitor(job)
counts = job.result().get_counts()

print(counts)

Introduction to the U gate in Qiskit with Code

Introduction

What is the U gate?

Implementation

How to run the program

Code

Output