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123 lines
4.3 KiB
Python
Executable File
123 lines
4.3 KiB
Python
Executable File
#!/usr/bin/env python3
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"""
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Deutsch-Josza Algorithm is one of the first examples of a quantum
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algorithm that is exponentially faster than any possible deterministic
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classical algorithm
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Premise:
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We are given a hidden Boolean function f,
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which takes as input a string of bits, and returns either 0 or 1:
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f({x0,x1,x2,...}) -> 0 or 1, where xn is 0 or 1
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The property of the given Boolean function is that it is guaranteed to
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either be balanced or constant. A constant function returns all 0's
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or all 1's for any input, while a balanced function returns 0's for
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exactly half of all inputs and 1's for the other half. Our task is to
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determine whether the given function is balanced or constant.
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References:
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- https://en.wikipedia.org/wiki/Deutsch-Jozsa_algorithm
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- https://qiskit.org/textbook/ch-algorithms/deutsch-jozsa.html
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"""
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import numpy as np
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import qiskit as q
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def dj_oracle(case: str, num_qubits: int) -> q.QuantumCircuit:
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"""
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Returns a Quantum Circuit for the Oracle function.
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The circuit returned can represent balanced or constant function,
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according to the arguments passed
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"""
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# This circuit has num_qubits+1 qubits: the size of the input,
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# plus one output qubit
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oracle_qc = q.QuantumCircuit(num_qubits + 1)
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# First, let's deal with the case in which oracle is balanced
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if case == "balanced":
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# First generate a random number that tells us which CNOTs to
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# wrap in X-gates:
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b = np.random.randint(1, 2**num_qubits)
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# Next, format 'b' as a binary string of length 'n', padded with zeros:
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b_str = format(b, f"0{num_qubits}b")
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# Next, we place the first X-gates. Each digit in our binary string
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# correspopnds to a qubit, if the digit is 0, we do nothing, if it's 1
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# we apply an X-gate to that qubit:
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for index, bit in enumerate(b_str):
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if bit == "1":
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oracle_qc.x(index)
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# Do the controlled-NOT gates for each qubit, using the output qubit
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# as the target:
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for index in range(num_qubits):
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oracle_qc.cx(index, num_qubits)
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# Next, place the final X-gates
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for index, bit in enumerate(b_str):
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if bit == "1":
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oracle_qc.x(index)
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# Case in which oracle is constant
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if case == "constant":
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# First decide what the fixed output of the oracle will be
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# (either always 0 or always 1)
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output = np.random.randint(2)
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if output == 1:
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oracle_qc.x(num_qubits)
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oracle_gate = oracle_qc.to_gate()
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oracle_gate.name = "Oracle" # To show when we display the circuit
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return oracle_gate
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def dj_algorithm(oracle: q.QuantumCircuit, num_qubits: int) -> q.QuantumCircuit:
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"""
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Returns the complete Deustch-Jozsa Quantum Circuit,
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adding Input & Output registers and Hadamard & Measurement Gates,
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to the Oracle Circuit passed in arguments
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"""
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dj_circuit = q.QuantumCircuit(num_qubits + 1, num_qubits)
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# Set up the output qubit:
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dj_circuit.x(num_qubits)
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dj_circuit.h(num_qubits)
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# And set up the input register:
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for qubit in range(num_qubits):
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dj_circuit.h(qubit)
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# Let's append the oracle gate to our circuit:
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dj_circuit.append(oracle, range(num_qubits + 1))
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# Finally, perform the H-gates again and measure:
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for qubit in range(num_qubits):
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dj_circuit.h(qubit)
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for i in range(num_qubits):
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dj_circuit.measure(i, i)
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return dj_circuit
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def deutsch_jozsa(case: str, num_qubits: int) -> q.result.counts.Counts:
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"""
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Main function that builds the circuit using other helper functions,
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runs the experiment 1000 times & returns the resultant qubit counts
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>>> deutsch_jozsa("constant", 3)
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{'000': 1000}
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>>> deutsch_jozsa("balanced", 3)
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{'111': 1000}
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"""
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# Use Aer's qasm_simulator
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simulator = q.Aer.get_backend("qasm_simulator")
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oracle_gate = dj_oracle(case, num_qubits)
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dj_circuit = dj_algorithm(oracle_gate, num_qubits)
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# Execute the circuit on the qasm simulator
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job = q.execute(dj_circuit, simulator, shots=1000)
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# Return the histogram data of the results of the experiment.
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return job.result().get_counts(dj_circuit)
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if __name__ == "__main__":
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print(f"Deutsch Jozsa - Constant Oracle: {deutsch_jozsa('constant', 3)}")
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print(f"Deutsch Jozsa - Balanced Oracle: {deutsch_jozsa('balanced', 3)}")
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