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 an integer comparator in Qiskit for IBM quantum computers.

What is an integer comparator?

An integer comparator is a circuit that compares two integers. In Qiskit the integer comparator circuit relies on two’s complement implementation of binary subtraction.

Implementation

In this section we will go through the full implementation step by step.

Step 1: Import modules

The first step is to import the necessary modules as seen below:

from qiskit import QuantumRegister, ClassicalRegister
from qiskit import QuantumCircuit, execute
from qiskit.circuit.library import IntegerComparator
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 main circuit

The next step is to create the circuit.

For our quantum register we will only require 4 qubits and for the classical register we will only require 1 bit.

q = QuantumRegister(4,'q')
c = ClassicalRegister(1,'c')

circuit = QuantumCircuit(q,c)

Step 4: Set the value to be compared and initialize the comparator circuit

The next step is to set the comparison value that we wish to compare to the input value. For this tutorial we will set the comparison value to 3 as seen on the first line in the code below.

The second line is where we construct the comparator circuit where:

num_state_qubits is the number of qubits that will hold the integer
value is the integer we wish compare the register value against.
geq: A boolean flag that will check if the input value is >= to the comparison value when set to true. Otherwise will check if the value is < comparison value when set to false

a = 3

comparator = IntegerComparator(num_state_qubits=2, value=a, geq=True)

Step 5: Encode the input value on to the input qubits

Here we encode the binary value ‘11’ on to the input register (or 3 in decimal). This is done by applying Pauli-X gates to qubits 0 and 1. This will flip their states from |0〉 to |1〉.

circuit.x(q[0])
circuit.x(q[1])

Step 6: Apply the comparator and measure the qubits

The next step is to apply the comparator to our circuit and measure the output qubit. The first line applies the comparator while the second line measures the output qubit (in this case qubit 2).

circuit = circuit.compose(comparator)
circuit.measure(q[2],c[0])

Step 7: Run the job and retrieve the results

The last step is to run the job and retrieve the results.

The first line executes the job that will be sent to the backend device where:

circuit: Our constructed circuit
backend: Our backend device (in our case a local Aer simulator)
shots: The number of times we wish to run the circuit

The second line gets our measurements and the third line prints them.

job = execute(circuit, backend, shots=1)
counts = job.result().get_counts()
print(counts)

Code

from qiskit import QuantumRegister, ClassicalRegister
from qiskit import QuantumCircuit, execute
from qiskit.circuit.library import IntegerComparator
from qiskit import Aer


backend = Aer.get_backend('aer_simulator')

q = QuantumRegister(4,'q')
c = ClassicalRegister(1,'c')

circuit = QuantumCircuit(q,c)

a = 3

comparator = IntegerComparator(num_state_qubits=2, value=a, geq=True)

circuit.x(q[0])
circuit.x(q[1])

circuit = circuit.compose(comparator)

circuit.measure(q[2],c[0])

print(circuit)

job = execute(circuit, backend, shots=1)

counts = job.result().get_counts()

print("Comparing if qubit register is greater or equal to integer:",a)
print(counts)

Integer Comparison in Qiskit