Issue with optimizing for functionality of quantum CNOT gate

[buttercutter]

This is a question on an application of ceviche rather than ceviche's internal code implementation.

@momchilmm suggested me to post my question here.

May I ask why https://colab.research.google.com/drive/1DeBtiZzOBVW9lc-hUDVKvtdCv5E3rpWc?usp=sharing failed 50% of the simulation tests (scenarios 1 and 2) ?

Is the result correct? True
                  scenario  phase_target  expected_phase_shift  \
0  Control Off, Target Off      0.000000              0.000000   
1   Control On, Target Off      2.977278              0.000000   
2   Control Off, Target On     -2.825583              0.000000   
3    Control On, Target On     -3.135028              3.141593   

   phase_difference  is_correct  
0          0.000000        True  
1          2.977278       False  
2          2.825583       False  
3          0.006565        True  
Error Analysis:
[{'scenario': 'Control Off, Target On', 'Ez_target_mean': (-9.70835981670322e-12+6.131494119920508e-12j), 'phase_target': -2.825583200697805}]

References:

• Two-dimensional photonic crystal based optical CNOT gate
• A novel design of quantum CNOT based on photonic crystal

[buttercutter]

I am now debugging the optimization goal :

# Define the optimization objective
def objective(rho_flat):
    rho = rho_flat.reshape((Nx, Ny))
    # Apply projection and blurring to rho
    rho_processed = make_rho(rho, design_region, radius=3)
    eps_r_linear = epsr_min + (epsr_max - epsr_min) * rho_processed

    # Compute control field
    sim_control = create_simulation(eps_r_linear)
    Ez_control = sim_control.solve(source_control)[0]

    # Compute delta_eps_r based on control field
    delta_eps_r = kerr_effect(Ez_control, eps_r_linear, n2_array_anp)
    eps_r = eps_r_linear + delta_eps_r

    # Solve for total field
    total_source = source_control + source_target
    sim_total = create_simulation(eps_r)
    Ez = sim_total.solve(total_source)[0]

    # Extract the Ez field at the target output waveguide
    output_slice = (
        slice(-Npml - 20, -Npml),
        slice(target_waveguide_y - waveguide_width // 2, target_waveguide_y + waveguide_width // 2)
    )
    Ez_output_target = Ez[output_slice]
    Ez_output_target_mean = anp.mean(Ez_output_target)

    # Expected phase shift (π for 'Control On, Target On')
    expected_phase_shift = anp.pi

    # Compute the phase difference
    output_phase = anp.angle(Ez_output_target_mean)
    phase_difference = anp.mod(output_phase - expected_phase_shift + anp.pi, 2 * anp.pi) - anp.pi  # Between -π and π
    print(f"phase_difference = {phase_difference}")

    # Objective is the squared phase difference
    objective_value = phase_difference**2

    return objective_value

Besides, a human friend told me the following, do anyone find other issues with the simulation plots ?

They are using photonic crystal as mirror trapping light and propagate within line defect as waveguide. And some how use their dispersion to engineer the phases of light for constructing CNOT gate. If you just follow their simulation method you will get result. In your simulation, I could not see periodic air holes at all.
Another thing I would point out is, usually people excite the input and get maximized output waveguide with mode source, but your plot seems not showing mode of the input and waveguide........ please check you placed them properly......

[buttercutter]

@momchilmm : I have managed to get 3 out of 4 test case scenarios passing, still debugging the code.

              scenario          phase_target     expected_phase_shift  phase_difference  is_correct  
0  Control Off, Target Off      0.000000              0.000000                 0.000000       True
1   Control On, Target Off     -3.137816              0.000000                 3.137816      False
2   Control Off, Target On      0.001458              0.000000                 0.001458       True 
3    Control On, Target On     -3.137787              3.141593                 0.003806       True