Each column in the table corresponds to a different gate. Just start by playing the animations.
The dissipation coefficient is set to 1 in all simulations bellow. Therefore the time is dimensionless.
Two Blobs | Three Blobs | ||||
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Phase Gate | Population Gate | Phase Gate | 2-Population Gate | 3-Population Gate | |
Description | The right blob goes on a circle. | The two blobs collide. | The right blob goes on a circle. | Two of the three blobs collide. | The three blobs collide. |
Initial State | |α0⟩+|−α0⟩ | |α0⟩ | |α0⟩+|3√−1α0⟩+|3√−12α0⟩ | |α0⟩+2|3√−1α0⟩ | |α0⟩ |
Animation for α0=2 | |||||
Scaling of the Purity wrt α0 and T |
1−P∝α−1.8150T−0.976 |
1−P∝α−3.9450T−0.984 |
1−P∝α0.9670T−0.988 |
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Scaling of the Purity wrt α0 and v(the phase-space "speed" of the blobs) |
1−P∝α−1.8150v0.976 v∝1/T |
1−P∝α−3.9450v0.984 v∝1/T |
1−P∝α−0.0200v0.988 v∝α0/T |
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The plots from the animation | |||||
Other remarks | Only the area matters for the induced phase. The loss in purity also seems to scale with the area, given that the results for a single circle of area A and for two circles each of area A/2 were the same (the total area was the same, the path taken was √2 bigger). See the next table. | For a fixed α0 the worst imperfections induced during the evolution are closer to the center. | Strange artefacts for the outer most blob, maybe due to cutoff dimension being too low. | For a fixed α0 the imperfections are induces mainly on the way into and out of the collision (not during the collision itself). | |
Technical Details | Various, see the code. 15000 samples, N=80 cutoff for the (1-P) log log plot. 20000 samples, N=40 for the comparisons in the next table, 15000 samples, N=40 for the animation. | 60000 samples, N=40 cutoff | 200000 samples, N=55 cutoff (which is insufficient for α0>2.6) | 680000 samples, N=55 cutoff (possibly insufficient for these plots and animations) | 680000 samples, N=55 cutoff |
Computer Code Files | phase gate, population gate, animation | visualization, simulation | visualization, simulation | visualization, simulation |
Two Blobs, Only the Right One Moving | Two Blobs Moving in Opposite Directions | |
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Plots and animations for various radiuses of the circles. | ||
Description | The right blob goes on a circle. | Both blobs go on circles. The total area of the circles is the same as in the one-blob case. |
Scaling of the Purity wrt α0 and T |
1−P∝α−1.8150T−0.976 |
1−P∝α−1.7970T−0.974 |
The final relative phase between the blobs |
Total time T on the x axis |
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The final purity of the system |
Total time T on the x axis |
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The contrast between the final purities for both approaches |