SPARQ

Spiking Physics-in-the-loop Autonomous Reinforcement triage of Quantum emitters: the installable sparq package behind the manuscript "Closed-loop, event-driven machine learning for autonomous triage of single-photon emitters." The manuscript's companion repository, a-spiking-RL-triage-of-solid-state-single-photon-emitters, holds the experiment scripts, figure scripts and results that reproduce the paper; this repository is the software's home for development, releases and support.

Installation

pip install sparq-triage        # physics core (numpy, scipy)
pip install sparq-triage[ml]    # adds PyTorch for the estimators, twin and RL

The core (sparq.physics, sparq.exact, sparq.pulsed) imports without PyTorch: the analytic HBT correlation functions, the exact-statistics histogram twin, the master-equation reference and the pulsed comb analysis.

import numpy as np
from sparq import HBTConfig, sample_site, expected_histogram

rng = np.random.default_rng(0)
site = sample_site(rng, platform="NV")     # literature-anchored priors
mu = expected_histogram(site, T_s=5.0, cfg=HBTConfig())
print(site.g2_0, site.is_good, mu.shape)

Analyzing your own data

analyze_histogram runs the full conventional pipeline on any measured CW HBT histogram (dip centering, re-binning, flat-level normalization, multi-start fit) and reports g2(0) with a parametric-bootstrap confidence interval that propagates shot noise through every analysis step; analyze_pulsed does the same for pulsed combs via the peak-area method. Neither needs PyTorch.

from sparq import analyze_histogram
res = analyze_histogram(delay_ns, counts, T_s=30.0, n_bootstrap=200)
print(res["g2_0"], (res["g2_0_low"], res["g2_0_high"]),
      res["single_emitter_confident"])

Sequential certification and rigorous intervals

SPRTCertifier implements Wald's sequential probability ratio test on accumulating HBT histograms with exact Poisson log-likelihoods: acquisition stops the moment the evidence crosses the error-rate thresholds, which on twin benchmarks certifies bright sites in a fraction of a second instead of a fixed 30 s dwell, at the nominal error rates. profile_likelihood_ci gives a Wilks profile-likelihood confidence interval for g2(0) from the exact Poisson likelihood, honest at low counts where linearized fit errors are not. Both are torch-free; the plug-in-hypothesis caveat and the empirical validation are documented in the module.

from sparq import SPRTCertifier, profile_likelihood_ci
cert = SPRTCertifier(site_single, site_pair, alpha=0.05, beta=0.05)
while cert.update(new_counts, dt) == "continue":
    ...                                   # keep acquiring
print(cert.decision, cert.T_total, cert.expected_times())

Exact closed-form corrections (new in v0.4)

background_corrected_g2 inverts the Poissonian-background map g2_meas = 1 + rho^2 (g2_true - 1) (Brouri et al., Opt. Lett. 25, 1294 (2000)) -- exactly the forward model the package's own g2_zero(..., rho) applies, so the round trip is machine-exact and asserted in the tests; the correction maps confidence-interval endpoints through the same affine transform, truncates at the physical floor g2 = 0 without hiding the untruncated value, and refuses rho outside (0, 1]. signal_fraction builds rho from measured signal and background rates. deadtime_corrected_rate inverts the non-paralyzable dead-time throughput r_meas = r/(1 + r tau_d) -- the exact renewal-theory rate of the greedy dead-time pass in the Monte-Carlo detector chain, validated against it statistically -- and refuses measured rates at or beyond the saturation rate instead of extrapolating. All three are torch-free.

from sparq import background_corrected_g2, signal_fraction

rho = signal_fraction(signal_rate, background_rate)
res = background_corrected_g2(g2_measured, rho, ci=(lo, hi))
print(res["g2_corrected"], res["ci"])

Exact Bayesian posterior for g2(0) (new in v0.5)

bayesian_g2 completes the inferential toolbox: alongside the bootstrap (shot noise through the full pipeline) and the Wilks profile likelihood (frequentist, model-based), it returns the EXACT finite-count Bayesian posterior of the model-free quantity papers quote first -- the raw central-window g2, the zero-delay coincidence rate over the flat level. With independent Gamma priors on the two Poisson rates (Jeffreys by default) the posterior of the ratio is a scaled beta-prime law in closed form: density, quantiles, equal-tailed credible intervals and the triage verdict probability P[g2 < 1/2 | data] are exact expressions in four counts -- no sampling, no optimizer, no asymptotics, and no acquisition time needed (it cancels in the ratio). The docstring states the estimand honestly: a window average sits on top of the dip, so it upper-bounds g2(0); dip-shape-aware inference stays with profile_likelihood_ci.

from sparq import bayesian_g2
post = bayesian_g2(counts_on_grid)         # Jeffreys prior, 1-ns window
lo, hi = post.credible_interval(0.95)
print(post.median(), (lo, hi), post.prob_below(0.5))

Anchors in the test suite: the hand-built beta-prime law against SciPy's independent implementation to 1e-12; unit mass and closed-form moments by quadrature; the closed form against direct numerical marginalization of the exact Poisson likelihood; Monte-Carlo Gamma-ratio agreement; nominal credible-interval coverage on twin-generated histograms; and the single-versus-two-emitter verdict ordering.

Registering your own platform

The built-in priors (NV, hBN, GaN, SiV) are literature-anchored defaults, not a limit: register_platform adds any emitter with your own photophysical ranges, after which it works everywhere a platform name is accepted (site sampling, the dataset generators, the triage environment, the graph encoder's template).

from sparq import Platform, register_platform, sample_site
register_platform(Platform("MyQD", (0.5, 2.0), (20, 400), (0.0, 0.5),
                           (50, 500), (0.7, 0.99), 0.05, (5, 100), (0.5, 10)))
site = sample_site(rng, platform="MyQD")

What is in the package

sparq/
  physics.py            emitter photophysics, platform priors, HBT twin
                        (exact Poisson histogram statistics) and the full
                        Monte-Carlo photon-stream simulator w/ detector
                        impairments
  exact.py              numerically exact master-equation g2(tau)
  pulsed.py             pulsed-excitation twin + comb calibration +
                        conventional peak-area analysis
  analysis.py           g2 analysis of measured data: bootstrap and
                        profile-likelihood uncertainties, exact
                        background and dead-time corrections (torch-free)
  sequential.py         Wald SPRT certifier on exact Poisson likelihoods
                        (torch-free)
  bayes.py              exact-Poisson Bayesian posterior of the raw
                        central-window g2 (conjugate closed form,
                        torch-free)
  datasets.py           synthetic acquisition generators + loader for the
                        real sps-quality quantum-dot HBT data
  estimators.py         LM-fit baseline, CNN, surrogate-gradient spiking
                        network, physics-in-the-loop training
  twin_torch.py         differentiable twin (adjoint/pathwise gradients
                        through the measurement protocol) + profile
                        Fisher information
  sac_per.py            discrete-action Soft Actor-Critic + prioritized
                        experience replay (sum-tree)
  rl_env.py             closed-loop emitter-triage environment + baselines
  gnn.py                level-structure template graphs + message-passing
                        encoder for cross-platform transfer

Tests

pip install -e .[test]
pytest tests -q     # a few seconds; ML tests skip when torch is absent

The suite pins the physics to exact references: the two-exponential g2 law against the master-equation eigen-decomposition, the closed-form IRF convolution against brute-force quadrature, Poisson statistics of the histogram twin, comb calibration and peak-area recovery, sum-tree replay proportionality, the exact background/dead-time correction round trips, the closed-form Bayesian g2 posterior against SciPy's independent beta-prime implementation and a direct Poisson marginalization, and the shape/gradient contracts of the estimators, the differentiable protocol twin and the triage environment. It runs in CI on every push and pull request.

Real data

The experimental quantum-dot HBT measurements used by sparq.datasets.load_fisequr are from the openly licensed sps-quality repository (Kedziora et al., Mach. Learn.: Sci. Technol. 4, 045042 (2023)); they are not redistributed here.

Contributing and support

Bug reports, questions and pull requests are welcome through GitHub issues; see CONTRIBUTING.md for the development setup and the design rules. Tagged releases are published to PyPI by CI.

License and citation

Apache-2.0 (see LICENSE). Please cite the associated paper if you use this code; citation metadata is in CITATION.cff.