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81 lines
2.0 KiB
Python
81 lines
2.0 KiB
Python
from __future__ import annotations
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from dataclasses import dataclass
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from typing import Tuple
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import math
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import cmath
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@dataclass
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class Qubit:
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"""
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A simple representation of a qubit for algorithm demonstrations.
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Attributes
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----------
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alpha : complex
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Amplitude of the |0> basis state.
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beta : complex
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Amplitude of the |1> basis state.
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"""
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alpha: complex
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beta: complex
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def normalize(self) -> None:
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"""
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Normalize the qubit so that |alpha|^2 + |beta|^2 = 1.
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"""
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norm = math.sqrt(abs(self.alpha)**2 + abs(self.beta)**2)
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if norm == 0:
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raise ValueError("Cannot normalize a zero vector.")
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self.alpha /= norm
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self.beta /= norm
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def hadamard(qubit: Qubit) -> Qubit:
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"""
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Apply the Hadamard gate to a single qubit.
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The Hadamard transform creates superposition: H|0> = (|0> + |1>)/sqrt(2), H|1> = (|0> - |1>)/sqrt(2).
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Parameters
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----------
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qubit : Qubit
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The input qubit to transform.
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Returns
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-------
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Qubit
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A new qubit after applying the Hadamard gate.
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"""
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inv_sqrt2 = 1.0 / math.sqrt(2)
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new_alpha = inv_sqrt2 * (qubit.alpha + qubit.beta)
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new_beta = inv_sqrt2 * (qubit.alpha - qubit.beta)
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return Qubit(alpha=new_alpha, beta=new_beta)
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def phase_shift(qubit: Qubit, theta: float) -> Qubit:
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"""
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Apply a phase shift gate to the |1> component of a qubit.
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Parameters
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----------
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qubit : Qubit
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The input qubit.
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theta : float
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Phase angle in radians.
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Returns
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-------
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Qubit
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A new qubit with the |1> component phase-shifted.
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"""
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return Qubit(alpha=qubit.alpha, beta=qubit.beta * cmath.exp(1j * theta))
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if __name__ == "__main__":
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# Example: apply Hadamard to |0> and then a phase shift of π/2
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q0 = Qubit(alpha=1+0j, beta=0+0j)
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hq = hadamard(q0)
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print("After Hadamard:", hq)
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pq = phase_shift(hq, math.pi / 2)
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print("After phase shift (\u03c0/2):", pq)
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