| """Regenerate synthetic data and publication figures; no experimental records.""" |
| from __future__ import annotations |
| import csv, json, pathlib, sys |
| import numpy as np |
| import matplotlib |
| matplotlib.use('Agg') |
| import matplotlib.pyplot as plt |
| from scipy.constants import h, k as k_B |
| from lioraen_omega import (phase_model, reflection, sigma, pick_matrices, |
| spectral_mass_bound, recover, full_response, quadratic_value, controls) |
| ROOT=pathlib.Path(__file__).resolve().parents[1] |
| SEED=16102027 |
|
|
| def write_csv(path, header, rows): |
| with path.open('w',newline='',encoding='utf-8') as f: |
| writer=csv.writer(f);writer.writerow(header);writer.writerows(rows) |
|
|
| def save_fig(name): |
| plt.tight_layout() |
| plt.savefig(ROOT/'manuscript'/'figures'/f'{name}.pdf',bbox_inches='tight') |
| plt.savefig(ROOT/'manuscript'/'figures'/f'{name}.png',dpi=160,bbox_inches='tight') |
| plt.close() |
|
|
| def main(): |
| rng=np.random.default_rng(SEED) |
| for directory in ['physics','data','results','manuscript/figures']: |
| (ROOT/directory).mkdir(parents=True,exist_ok=True) |
| eta=.05;kext=.05;tau=.2;phis=[np.pi/2,-np.pi/2] |
| models=[phase_model(p) for p in phis] |
| omegas=np.linspace(-1.2,1.2,801) |
| values=np.array([[reflection(*model,float(w),1j*tau,eta,kext) |
| for w in omegas] for model in models]) |
| contrast=np.abs(values[0]-values[1]);index=int(np.argmax(contrast));w0=float(omegas[index]) |
| std_single=.001; repeats=25;std_mean=std_single/np.sqrt(repeats) |
| noisy=values+std_mean/np.sqrt(2)*(rng.normal(size=values.shape)+1j*rng.normal(size=values.shape)) |
| rows=[] |
| for j,w in enumerate(omegas): |
| rows.append([w,values[0,j].real,values[0,j].imag,values[1,j].real, |
| values[1,j].imag,contrast[j],noisy[0,j].real,noisy[0,j].imag, |
| noisy[1,j].real,noisy[1,j].imag]) |
| write_csv(ROOT/'physics'/'phase_scan.csv', |
| ['omega_over_Omega0','S_plus_real','S_plus_imag','S_minus_real','S_minus_imag', |
| 'absolute_contrast','noisy_plus_real','noisy_plus_imag', |
| 'noisy_minus_real','noisy_minus_imag'],rows) |
| plt.figure(figsize=(7.0,4.2)) |
| plt.plot(omegas,np.abs(values[0]),label=r'$\phi=+\pi/2$') |
| plt.plot(omegas,np.abs(values[1]),label=r'$\phi=-\pi/2$') |
| plt.xlabel(r'Drive detuning $\omega/\Omega_0$');plt.ylabel('Reflection amplitude magnitude') |
| plt.title('Synthetic phase-controlled one-port response');plt.legend() |
| save_fig('reflection_phase') |
| plt.figure(figsize=(7.0,4.2)) |
| plt.plot(omegas,contrast) |
| plt.xlabel(r'Drive detuning $\omega/\Omega_0$');plt.ylabel(r'$|S_{+}-S_{-}|$') |
| plt.title('Synthetic complex-reflection contrast') |
| save_fig('phase_contrast') |
| |
| ts=[tau*t for t in controls(1)];H,L,C=models[0];z=w0+1j*eta |
| fs=[full_response(H,L,C,z,t) for t in ts] |
| cal_records=[];fmeas=[] |
| for j,(t,f) in enumerate(zip(ts,fs)): |
| sexact=1-1j*kext/f |
| sm=sexact+std_mean/np.sqrt(2)*(rng.normal()+1j*rng.normal()) |
| gm=(1-sm)/(1j*kext);fm=1/gm;fmeas.append(fm) |
| cal_records.append([j,t[0].real,t[0].imag,sexact.real,sexact.imag, |
| sm.real,sm.imag,f.real,f.imag,fm.real,fm.imag]) |
| write_csv(ROOT/'physics'/'raw_control_records.csv', |
| ['setting','t_real','t_imag','S_exact_real','S_exact_imag','S_measured_real', |
| 'S_measured_imag','F_exact_real','F_exact_imag','F_measured_real', |
| 'F_measured_imag'],cal_records) |
| rec=recover(ts,fs);recnoise=recover(ts,fmeas) |
| withheld=[] |
| for j in range(20): |
| t=tau*(rng.normal(size=1)+1j*rng.normal(size=1)) |
| truth=full_response(H,L,C,z,t);pred=quadratic_value(rec,t) |
| noisy_pred=quadratic_value(recnoise,t) |
| |
| Ldrift=L.copy();Ldrift[0,0]+=.025 |
| drift=full_response(H,Ldrift,C,z,t) |
| withheld.append([j,t[0].real,t[0].imag,truth.real,truth.imag, |
| abs(pred-truth),abs(noisy_pred-truth),abs(pred-drift)]) |
| write_csv(ROOT/'physics'/'withheld_controls.csv', |
| ['index','t_real','t_imag','F_true_real','F_true_imag','exact_prediction_error', |
| 'noisy_prediction_error','deliberate_drift_error'],withheld) |
| |
| times=np.linspace(0,10,501) |
| mem=np.array([abs(np.exp(.6j*times)+np.exp(1j*p)*np.exp(-.6j*times))**2 for p in phis]) |
| write_csv(ROOT/'data'/'memory_phase.csv',['time_times_Omega0','plus','minus'], |
| zip(times,mem[0],mem[1])) |
| plt.figure(figsize=(7,4.2)) |
| for p,m in zip(phis,mem): |
| plt.plot(times,m,label=r'$\phi=+\pi/2$' if p>0 else r'$\phi=-\pi/2$') |
| plt.xlabel(r'Dimensionless time $t\Omega_0$');plt.ylabel(r'$|\mathcal{M}_{12}(t)|^2/g^4$') |
| plt.legend();plt.title('A phase relation across two spectral poles') |
| save_fig('memory_phase') |
| ns=np.arange(1,9);profile=np.minimum(ns,3)+2*np.minimum(ns,2) |
| write_csv(ROOT/'data'/'rank_profiles.csv',['nodes','seven_state_Hermitian','one_damped_state'],zip(ns,profile,ns)) |
| plt.figure(figsize=(7,4.2)) |
| plt.plot(ns,profile,'o-',label='Seven-state Hermitian model (q=3)') |
| plt.plot(ns,ns,'s--',label='One damped state, unshifted kernel (q=1)') |
| plt.xlabel('Number of distinct sample frequencies');plt.ylabel('Exact kernel rank') |
| plt.xticks(ns);plt.legend();plt.title('Completion versus persistent rank growth') |
| save_fig('rank_profiles') |
| zs=np.linspace(-2,2,8)+.7j;gamma=.4 |
| vals=[np.array([[1/(z+1j*gamma)]]) for z in zs] |
| K,_,_=pick_matrices(zs,vals);Kcorrect,_,_=pick_matrices(zs+1j*gamma,vals) |
| eig=np.linalg.eigvalsh(K)[::-1];correct=np.linalg.eigvalsh(Kcorrect)[::-1] |
| write_csv(ROOT/'data'/'damping_kernel_spectrum.csv', |
| ['index','uncorrected_eigenvalue','known_shift_eigenvalue'],zip(range(1,9),eig,correct)) |
| plt.figure(figsize=(7,4.2)) |
| plt.semilogy(range(1,9),np.maximum(abs(eig),1e-18),'o-',label='Unshifted Pick kernel') |
| plt.semilogy(range(1,9),np.maximum(abs(correct),1e-18),'s--',label='Known common linewidth shift') |
| plt.xlabel('Eigenvalue index');plt.ylabel('Absolute numerical eigenvalue') |
| plt.legend();plt.title('One damped mode: two different dimension questions') |
| save_fig('damping_spectrum') |
| |
| wz=np.array([-.7+.5j,0+.5j,.7+.5j]);roots=np.array([-.5,.5]) |
| masses=np.array([1.,1.,1e-6]);poles=np.array([-.5,.5,.9]) |
| vals=[np.array([[sum(masses/(z-poles))]]) for z in wz] |
| Kw,_,_=pick_matrices(wz,vals) |
| result=spectral_mass_bound(wz,roots,Kw,1,1.,.2,sample_error=1e-10) |
| result['weights']=[[float(a.real),float(a.imag)] for a in result['weights']] |
| result.update(actual_outside_mass=1e-6,total_mass=float(sum(masses)), |
| support_radius=1.,band_radius=.2,assumed_sample_error=1e-10) |
| assert result['bound']>=result['actual_outside_mass'] |
| (ROOT/'results'/'spectral_witness.json').write_text(json.dumps(result,indent=2)+'\n') |
| occupation=float(1/np.expm1(h*10e6/(k_B*.01))) |
| real_null=max(abs(full_response(*models[0],z,[x])-full_response(*models[1],z,[x])) |
| for x in np.linspace(-.5,.5,31)) |
| report=dict(status='entirely synthetic; no physical experiment',seed=SEED, |
| angular_frequency_unit_rad_per_s=float(2*np.pi*1e6), |
| parameter_units='Hamiltonian, linewidth, and drive detuning divided by Omega0', |
| eta=.05,kappa_external=.05,g=.3,tau=.2, |
| visible_detunings=[-.1,.15],hidden_detunings=[-.6,.6], |
| maximum_complex_reflection_contrast=float(contrast[index]), |
| omega_at_maximum=w0,frequency_grid_points=len(omegas), |
| maximum_absolute_reflection=float(abs(values).max()), |
| real_control_transpose_null_max=float(real_null), |
| assumed_single_record_complex_rms=std_single,repeats=repeats, |
| assumed_averaged_complex_rms=std_mean,assumed_systematic_target=.005, |
| thermal_example=dict(frequency_Hz=10e6,temperature_K=.01,occupation=occupation), |
| control_design_condition=rec['condition'], |
| maximum_exact_withheld_error=float(max(row[5] for row in withheld)), |
| maximum_noisy_withheld_error=float(max(row[6] for row in withheld)), |
| minimum_deliberate_drift_error=float(min(row[7] for row in withheld)), |
| maximum_deliberate_drift_error=float(max(row[7] for row in withheld)), |
| witness_bound=float(result['bound'])) |
| assert report['maximum_absolute_reflection']<=1+1e-10 |
| assert real_null<1e-10 |
| assert report['maximum_exact_withheld_error']<1e-8 |
| (ROOT/'physics'/'parameters_and_results.json').write_text(json.dumps(report,indent=2)+'\n') |
| tex=(r'\newcommand{\PeakContrast}{'+f"{report['maximum_complex_reflection_contrast']:.4f}"+'}\n'+ |
| r'\newcommand{\PeakFrequency}{'+f'{w0:.3f}'+'}\n'+ |
| r'\newcommand{\ThermalOccupation}{'+f'{occupation:.2f}'+'}\n'+ |
| r'\newcommand{\WitnessBound}{'+f"{result['bound']:.6f}"+'}\n') |
| (ROOT/'manuscript'/'generated_numbers.tex').write_text(tex) |
| print(json.dumps(report,indent=2)) |
| if __name__=='__main__':main() |
|
|
