mirror of
https://github.com/vale981/HOPSFlow-Paper
synced 2025-03-05 09:41:40 -05:00
207 lines
6.9 KiB
Org Mode
207 lines
6.9 KiB
Org Mode
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:PROPERTIES:
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:ID: 66cb884e-8724-488d-88da-21b929ffc2bb
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:END:
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#+PROPERTY: header-args :session otto_relax :kernel python :pandoc no :async yes :tangle tangle/otto_relax.py
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In here, we'll try to find out how long the cycle has to be, to ensure
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complete thermalization.
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* Boilerplate
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#+name: boilerplate
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#+begin_src jupyter-python :results none
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import figsaver as fs
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import plot_utils as pu
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from hiro_models.one_qubit_model import StocProcTolerances
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from hiro_models.otto_cycle import OttoEngine
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import hiro_models.model_auxiliary as aux
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import numpy as np
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import qutip as qt
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import utilities as ut
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import stocproc
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import matplotlib.pyplot as plt
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import otto_utilities as ot
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import ray
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ray.shutdown()
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#ray.init(address='auto')
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ray.init()
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from hops.util.logging_setup import logging_setup
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import logging
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logging_setup(logging.INFO)
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plt.rcParams['figure.figsize'] = (12,4)
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#+end_src
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* Cycle
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This model reflects the currently "best-working" configuration. The
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only parameter we'll vary is the cycle time θ. We'll be interested in
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whether the system thermalizes.
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Therefore we need a way to keep the coupling switching speed constant.
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#+begin_src jupyter-python :results none
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def timings(τ_c, τ_i):
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τ_th = (1 - 2 * τ_c) / 2
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τ_i_on = τ_th - 2 * τ_i
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timings_H = (0, τ_c, τ_c + τ_th, 2 * τ_c + τ_th)
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timings_L_hot = (τ_c, τ_c + τ_i, τ_c + τ_i + τ_i_on, τ_c + 2 * τ_i + τ_i_on)
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timings_L_cold = tuple(time + timings_H[2] for time in timings_L_hot)
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return timings_H, (timings_L_cold, timings_L_hot)
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#+end_src
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Now we define the prototype. The numeric accuracy is jacked down, as
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we don't need precision. We only use two cycles because of the long
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cycle time. With δ=.4 θ=70 seemed ok. So let's try with .6 and 50
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ok. 1 and 40 is ok too. Let's try 1 and 45. Seems OK, but let's ease
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off on the coupling strength and try .8.
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#+begin_src jupyter-python
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def make_cycle(θ):
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(p_H, p_L) = timings(3. / θ, 3. / θ)
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return OttoEngine(
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δ=[.8, .8],
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ω_c=[2, 2],
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ψ_0=qt.basis([2], [1]),
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description=f"Classic Cycle",
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k_max=4,
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bcf_terms=[4] * 2,
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truncation_scheme="simplex",
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driving_process_tolerances=[StocProcTolerances(1e-3, 1e-3)] * 2,
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thermal_process_tolerances=[StocProcTolerances(1e-3, 1e-3)] * 2,
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T=[0.5, 4],
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therm_methods=["tanhsinh", "tanhsinh"],
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Δ=1,
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num_cycles=2,
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Θ=θ,
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dt=0.001,
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timings_H=p_H,
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timings_L=p_L,
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streaming_mode=True,
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shift_to_resonance=(False, False),
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L_shift=(0, 0),
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)
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#+end_src
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#+RESULTS:
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#+begin_src jupyter-python :tangle no
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ot.plot_cycle(make_cycle(100))
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#+end_src
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#+RESULTS:
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:RESULTS:
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| <Figure | size | 1200x400 | with | 1 | Axes> | <AxesSubplot: | xlabel= | $\tau$ | ylabel= | Operator Norm | > |
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[[file:./.ob-jupyter/e0c333c986674c4d0bcb9fafbd5cd47a6fa77210.svg]]
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:END:
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* Cursory Scanning
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We can now test the model to find wether it allows enough time for
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complete thermalization. We'll start with a really long cycle.
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We tried 100, now we try 60. 60 is a bit too short. So let's try 70
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#+begin_src jupyter-python :results none
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long_cycle = make_cycle(45)
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#+end_src
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#+begin_src jupyter-python
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ot.integrate_online(long_cycle, 100_000)
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#+end_src
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#+RESULTS:
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We can also import from taurus.
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#+begin_src jupyter-python :tangle no
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from hiro_models.model_auxiliary import import_results
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import_results(
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other_data_path="./taurus/.data",
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other_results_path="./taurus/results",
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interactive=False,
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models_to_import=[long_cycle],
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force=True,
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)
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#+end_src
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#+RESULTS:
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Now we look at the system energy.
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#+begin_src jupyter-python
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f, a, *_ = pu.plot_with_σ(long_cycle.t, long_cycle.system_energy())
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a.set_xlim(0, long_cycle.Θ)
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#+end_src
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#+RESULTS:
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:RESULTS:
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| 0.0 | 45.0 |
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[[file:./.ob-jupyter/3690e1e23aa7103ad49ab3612aa2b0baaa1e5dad.svg]]
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:END:
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[[file:./.ob-jupyter/2c1a4d916249a5998d36181e93f93a3a46712b94.svg]]
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#+begin_src jupyter-python
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ot.plot_energy(long_cycle)
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#+end_src
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#+RESULTS:
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:RESULTS:
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| <Figure | size | 1200x400 | with | 1 | Axes> | <AxesSubplot: | xlabel= | $\tau$ | ylabel= | Energy | > |
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[[file:./.ob-jupyter/7fa0ef03b52d099133087281c56b939c001c3563.svg]]
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:END:
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#+begin_src jupyter-python
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pu.plot_with_σ(long_cycle.t, long_cycle.bath_energy_flow().sum_baths())
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#+end_src
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#+RESULTS:
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:RESULTS:
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| <Figure | size | 1200x400 | with | 1 | Axes> | <AxesSubplot: | > | ((<matplotlib.lines.Line2D at 0x7fb4f3b63bb0>) <matplotlib.collections.PolyCollection at 0x7fb4f3b73d00>) |
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[[file:./.ob-jupyter/6b4e457a1dd6b1339a8fe78be12d02718f63d2d4.svg]]
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:END:
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We would like to know how far away from the thermal state the system is.
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#+begin_src jupyter-python :results none
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def thermal_state(Ω, T):
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ρ = np.array([[np.exp(-Ω/T), 0], [0, 1]])
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ρ /= np.sum(np.diag(ρ))
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return ρ
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#+end_src
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#+begin_src jupyter-python
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import hops.util.utilities
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from hopsflow.util import EnsembleValue
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with aux.get_data(long_cycle) as data:
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trace_dist_c = hops.util.utilities.trace_distance(data, relative_to=thermal_state(long_cycle.T[0], long_cycle.energy_gaps[0]))
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trace_dist_h = hops.util.utilities.trace_distance(data, relative_to=thermal_state(long_cycle.T[1], long_cycle.energy_gaps[1]))
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f, a = plt.subplots()
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pu.plot_with_σ(long_cycle.t, EnsembleValue(trace_dist_c), ax=a, label=r"$||\rho(\tau)-\rho_c||$")
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pu.plot_with_σ(long_cycle.t, EnsembleValue(trace_dist_h), ax=a, label=r"$||\rho(\tau)-\rho_h||$")
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a.plot(long_cycle.t, (long_cycle.H(long_cycle.t)[:, 0, 0] - 1)/2, label="H Modulation")
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a.set_xlabel(r"$\tau$")
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#a.set_xlim(155)
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a.legend()
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fs.export_fig("thermalization")
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#+end_src
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#+RESULTS:
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:RESULTS:
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: /nix/store/vkzza81mzwyk5br1c6cm67g48xycvmvl-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1369: ComplexWarning: Casting complex values to real discards the imaginary part
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: return np.asarray(x, float)
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: /nix/store/vkzza81mzwyk5br1c6cm67g48xycvmvl-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5340: ComplexWarning: Casting complex values to real discards the imaginary part
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: pts[0] = start
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: /nix/store/vkzza81mzwyk5br1c6cm67g48xycvmvl-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5341: ComplexWarning: Casting complex values to real discards the imaginary part
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: pts[N + 1] = end
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: /nix/store/vkzza81mzwyk5br1c6cm67g48xycvmvl-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5344: ComplexWarning: Casting complex values to real discards the imaginary part
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: pts[1:N+1, 1] = dep1slice
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: /nix/store/vkzza81mzwyk5br1c6cm67g48xycvmvl-python3-3.9.15-env/lib/python3.9/site-packages/matplotlib/axes/_axes.py:5346: ComplexWarning: Casting complex values to real discards the imaginary part
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: pts[N+2:, 1] = dep2slice[::-1]
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[[file:./.ob-jupyter/ed0b6c9c04abab45ec849730cf1d7ed025ece4e8.svg]]
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:END:
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