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#!/usr/bin/env python3

"""

Deutsch-Josza Algorithm is one of the first examples of a quantum

algorithm that is exponentially faster than any possible deterministic

classical algorithm

Premise:

We are given a hidden Boolean function f,

which takes as input a string of bits, and returns either 0 or 1:

f({x0,x1,x2,...}) -> 0 or 1, where xn is 0 or 1

The property of the given Boolean function is that it is guaranteed to

either be balanced or constant. A constant function returns all 0's

or all 1's for any input, while a balanced function returns 0's for

exactly half of all inputs and 1's for the other half. Our task is to

determine whether the given function is balanced or constant.

References:

- https://en.wikipedia.org/wiki/Deutsch-Jozsa_algorithm

- https://qiskit.org/textbook/ch-algorithms/deutsch-jozsa.html

"""

import numpy as np

import qiskit as q

def dj_oracle(case: str, num_qubits: int) -> q.QuantumCircuit:

"""

Returns a Quantum Circuit for the Oracle function.

The circuit returned can represent balanced or constant function,

according to the arguments passed

"""

# This circuit has num_qubits+1 qubits: the size of the input,

# plus one output qubit

oracle_qc = q.QuantumCircuit(num_qubits + 1)

# First, let's deal with the case in which oracle is balanced

if case == "balanced":

# First generate a random number that tells us which CNOTs to

# wrap in X-gates:

b = np.random.randint(1, 2 ** num_qubits)

# Next, format 'b' as a binary string of length 'n', padded with zeros:

b_str = format(b, f"0{num_qubits}b")

# Next, we place the first X-gates. Each digit in our binary string

# correspopnds to a qubit, if the digit is 0, we do nothing, if it's 1

# we apply an X-gate to that qubit:

for index, bit in enumerate(b_str):

if bit == "1":

oracle_qc.x(index)

# Do the controlled-NOT gates for each qubit, using the output qubit

# as the target:

for index in range(num_qubits):

oracle_qc.cx(index, num_qubits)

# Next, place the final X-gates

for index, bit in enumerate(b_str):

if bit == "1":

oracle_qc.x(index)

# Case in which oracle is constant

if case == "constant":

# First decide what the fixed output of the oracle will be

# (either always 0 or always 1)

output = np.random.randint(2)

if output == 1:

oracle_qc.x(num_qubits)

oracle_gate = oracle_qc.to_gate()

oracle_gate.name = "Oracle" # To show when we display the circuit

return oracle_gate

def dj_algorithm(oracle: q.QuantumCircuit, num_qubits: int) -> q.QuantumCircuit:

"""

Returns the complete Deustch-Jozsa Quantum Circuit,

adding Input & Output registers and Hadamard & Measurement Gates,

to the Oracle Circuit passed in arguments

"""

dj_circuit = q.QuantumCircuit(num_qubits + 1, num_qubits)

# Set up the output qubit:

dj_circuit.x(num_qubits)

dj_circuit.h(num_qubits)

# And set up the input register:

for qubit in range(num_qubits):

dj_circuit.h(qubit)

# Let's append the oracle gate to our circuit:

dj_circuit.append(oracle, range(num_qubits + 1))

# Finally, perform the H-gates again and measure:

for qubit in range(num_qubits):

dj_circuit.h(qubit)

for i in range(num_qubits):

dj_circuit.measure(i, i)

return dj_circuit

def deutsch_jozsa(case: str, num_qubits: int) -> q.result.counts.Counts:

"""

Main function that builds the circuit using other helper functions,

runs the experiment 1000 times & returns the resultant qubit counts

>>> deutsch_jozsa("constant", 3)

{'000': 1000}

>>> deutsch_jozsa("balanced", 3)

{'111': 1000}

"""

# Use Aer's qasm_simulator

simulator = q.Aer.get_backend("qasm_simulator")

oracle_gate = dj_oracle(case, num_qubits)

dj_circuit = dj_algorithm(oracle_gate, num_qubits)

# Execute the circuit on the qasm simulator

job = q.execute(dj_circuit, simulator, shots=1000)

# Return the histogram data of the results of the experiment.

return job.result().get_counts(dj_circuit)

if __name__ == "__main__":

print(f"Deutsch Jozsa - Constant Oracle: {deutsch_jozsa('constant', 3)}")

print(f"Deutsch Jozsa - Balanced Oracle: {deutsch_jozsa('balanced', 3)}")

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