101 lines
3.2 KiB
Python
101 lines
3.2 KiB
Python
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import matplotlib.pyplot as plt
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from lib import *
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def plot(t, s):
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fig, ax = plt.subplots()
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ax.plot(t, s)
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ax.set(xlabel='angle', ylabel='result', title='plot')
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ax.grid()
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fig.savefig("test.png")
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plt.show()
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# Double-slit, which-way
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# https://physics.stackexchange.com/questions/229895/understanding-the-quantum-eraser-from-a-quantum-information-stand-point
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# Delayed-choice quantum eraser:
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# https://quantumcomputing.stackexchange.com/questions/1568/what-is-the-quantum-circuit-equivalent-of-a-delayed-choice-quantum-eraser
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# The matrix
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# Λ=eiϕ/2|0⟩⟨0|+e−iϕ/2|1⟩⟨1|
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# introduces a phase shift between the two paths (this can e.g. be a
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# function of the position on the screen, or the relative length of
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# the interferometer arms)
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# See note on the post:
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# you could use quirk to provide interactive versions of the quantum
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# circuits. For example, your first circuit is this
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# https://algassert.com/quirk#circuit={%22cols%22:[[%22H%22],[%22Z^t%22],
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# [%22H%22],[%22Measure%22]]}
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# , while your second is
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# https://algassert.com/quirk#circuit=%7B%22cols%22:%5B%5B%22H%22%5D,
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# %5B%22%E2%80%A2%22,%22X%22%5D,%5B%22Z%5Et%22%5D,%5B%22H%22%5D%5D%7D
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# this.
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# Note(pisquared): The difference seems in the Lambda operator which
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# seems to be actually a [T-Gate](
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# https://www.quantum-inspire.com/kbase/t-gate/)
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# In quirk, the Z^t keeps |0><0| while the description
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# in the post spins |0><0| to oposite degrees which
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# cancels after application of the second H-gate
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def double_slit():
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"""
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#
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:return:
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"""
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ms = list()
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angles = np.arange(-4 * np.pi, 4 * np.pi, 0.1)
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for theta in angles:
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# Here, the first H puts the qubit in the superposition of both
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# paths/slits -- the states |0⟩ and |1⟩ correspond to the two
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# paths/slits
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phi1 = H.on(s("|0>"))
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phi2 = T(theta).on(phi1)
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# and the second H makes the two paths interfere.
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phi3 = H.on(phi2)
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# If the output qubit is measured in state |0⟩,
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# the interference is constructive, otherwise desctructive.
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#
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# You can easily check that this yields an interference pattern which
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# varies like prob(0)=cos(ϕ)2.
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ms.append(phi3.get_prob(0))
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# ms.append(phi3.measure())
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plot(angles, ms)
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def which_way():
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ms = list()
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angles = np.arange(-4 * np.pi, 4 * np.pi, 0.1)
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for theta in angles:
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# Here, the first H puts the qubit in the superposition of both
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# paths/slits -- the states |0⟩ and |1⟩ correspond to the two
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# paths/slits
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phi1 = H.on(s("|0>"))
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# Now imagine that we want to copy the which-way information:
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# Then, what we do is
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q2 = s("|0>")
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phi2 = CNOT.on(phi1 * q2)
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phi3 = T(theta).on(phi2, 0)
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phi4 = H.on(phi3, 0)
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# this is, we copy the which-way information before traversing the
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# interferometer onto qubit c. It is easy to see that this destroys
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# the interference pattern, i.e., prob(0)=1/2.
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ms.append(phi4.get_prob(0))
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# ms.append(phi3.measure())
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plot(angles, ms)
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if __name__ == "__main__":
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double_slit()
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which_way()
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