Construct a balanced Oracle and verify it using the Deutsch-Jozsa algorithm

[quantumadmin]

Let's construct a balanced oracle for the Deutsch-Jozsa algorithm and then use the algorithm to verify it. In the Deutsch-Jozsa algorithm, a balanced oracle will return '1' for exactly half of the possible input strings and '0' for the other half.

Here's the code to construct and verify a balanced oracle using Qiskit:

Code: Select all

from qiskit import QuantumCircuit, Aer, execute

# Define the number of input qubits (n) and 1 ancillary qubit
n = 3

# Create a quantum circuit with n+1 qubits (n input qubits and 1 ancillary qubit)
circuit = QuantumCircuit(n+1)

# Apply Hadamard gates to input qubits and the ancillary qubit
circuit.h(range(n+1))

# Apply the balanced oracle
# In a balanced oracle, the ancillary qubit is controlled by the input qubits.
# For half of the possible input strings, the oracle flips the ancillary qubit (applies X gate).
for i in range(n):
    if i % 2 == 0:
        circuit.cx(i, n)

# Apply Hadamard gates again to input qubits
circuit.h(range(n))

# Measure the input qubits
circuit.measure(range(n), range(n))

# Simulate the circuit
simulator = Aer.get_backend('qasm_simulator')
job = execute(circuit, simulator, shots=1)

# Get and print the measurement result
result = job.result().get_counts()
print("Measured Result:", result)

In this code, we create a balanced oracle by flipping the ancillary qubit for half of the possible input strings. The oracle is constructed using controlled-X (CX) gates. We then apply the Deutsch-Jozsa algorithm to verify whether the oracle is balanced or not.

Running this code should output a measurement result indicating that the oracle is balanced. The result should be in the form of {'000': 1} or {'001': 1}, indicating that all possible input strings led to the ancillary qubit being in state '1', which signifies a balanced oracle.

Feel free to modify the n variable to change the number of input qubits and experiment with different oracle constructions.