diff --git a/quantum/deutsch_jozsa.py b/quantum/deutsch_jozsa.py new file mode 100755 index 000000000..da1b6e4e9 --- /dev/null +++ b/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)}")