Implement Deutsch-Jozsa Algorithm In Qiskit (#3447)

* Implement Deutsch-Jozsa Algorithm In Qiskit

Signed-off-by: Abhishek Jaisingh <abhi2254015@gmail.com>

* Add Changes Requested In Review

Signed-off-by: Abhishek Jaisingh <abhi2254015@gmail.com>

* Address Further Review Comments

* fixup! Format Python code with psf/black push

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

quantum/deutsch_jozsa.py

@@ -0,0 +1,122 @@
+#!/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)}")