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1d047d9 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 | """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')
# Raw four-setting reconstruction and withheld checks use full resolvents.
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)
# An intentional hidden-mode shift only at validation invalidates the model.
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)
# Return-memory cross-pole invariant.
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')
# A nonvacuous but deliberately conservative support witness.
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()
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