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 explore the S gate and how to implement on IBM quantum devices in Qiskit.

The S gate (otherwise known as the √Z gate) is a gate that performs a rotation of π/2 around the Z axis. It is represented by the following matrix:

Much like the Z gate if we initialise the qubit to |0〉and apply an S gate the qubits state will remain |0〉:

However if we first initialise the qubits state to |1〉:

Which has transformed the state from |1〉to i|1〉

It is important to note that since the S gate performs a rotation of π/2 if we apply two S gates we will get the equivalent of a Z gate:

Applying the first S gate:

Then the second S gate:

Which gives us −|1〉. This is correct as if we applied a Z gate to a qubit that is initialized to |1〉we would also get −|1〉

Since two S gates are equivalent to a Z gate we can flip a qubit from |0〉to |1〉by putting the qubit in to superposition, applying two S gates and then applying a closing Hadamard gate. To see how this works let’s go through step by step.

First initialise the qubit and apply a Hadamard gate:

Which has put the qubit in to superposition. Now if we apply the first S gate:

Now if we apply the second S gate:

and finally if we apply the closing Hadamard gate:

Which gives us |1〉as the final state! Note the full code below if for this example.

Impementation

The S gate can be implemented very easily in Qiskit using the following line of code:

circuit.s(q[0])

Where q[0] is the qubit we are applying the S gate to.

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

IBMQ.enable_account('ENTER THE 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.h(q[0]) #Applying a Hadamard gate
circuit.s(q[0]) #Applying an S gate
circuit.s(q[0])
circuit.h(q[0]) #Applying another Hadamard gate to bring the qubit out of superposition
circuit.measure(q,c) #Measuring the qubit

print(circuit)

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

job_monitor(job)
counts = job.result().get_counts()

print(counts)

Introduction to the S gate in Qiskit with Code

Introduction

Impementation

How to run the program

Code

Output