A closer look at the science
From equations
to evidence.
Explore actual r34 numerical runs. Open a figure, inspect the assumptions, and download the configuration or reproduction bundle to repeat the study in your own research environment.
01 / Portable numerical relativity
Vacuum BSSN.
The gauge-wave link.
Follow a numerically evolved metric into a photon-link calculation and an illustrative quantum receiver model. Inspect fields, constraints and measured grid convergence.
Fourth-order centered finite differences and RK4 evolution, with harmonic lapse, zero shift and periodic boundaries. The gauge wave is flat spacetime in changing coordinates, rather than physical gravitational radiation. This is PF’s independent portable solver; the example does not execute Einstein Toolkit.
02 / Geometry to a quantum receiver
Connect the calculation.
A null link propagates through the saved numerical metric. Its frequency ratio then drives a declared Gaussian receiver-mode channel.
These outputs belong to the gauge-wave-link run above. They depend on its fixed illustrative receiver assumptions and do not establish intrinsic decoherence, hardware performance or a PF timing advantage.
03 / Quantum optics
Two photons.
One interference pattern.
Explore Hong–Ou–Mandel coincidence predictions as relative photon delay changes, with declared jitter, optical loss and detector efficiency.
The model uses 2,049 wavepacket quadrature points, order-24 jitter quadrature and an attempt rate of 100,000 Hz. Both numerical checks passed. These are model predictions, not experimental observations.
04 / Quantum characterization
See the channel
behind the outcome.
Compare amplitude damping, dephasing, depolarizing and Z-rotation channels using Qiskit density-matrix tomography and numerical reference checks.
Parameters are 0, 0.02, 0.1, 0.3 and 0.5: probabilities for the first three channels and radians for Z rotation. Exact model calculations avoid sampling noise here; they are not hardware measurements or certification.
05 / Satellite & quantum-link research
Follow the orbit.
Compare the prediction.
Use archived public orbital elements to reproduce satellite motion, then compare matched orbital models through actual photon and quantum-channel calculations.
Both orbit branches completed three scenarios at three epochs, with resolved propagation and Earth-clear geometry. The modeled source depolarization was 0.005; phase noise and storage were disabled. Conditional fidelity was 0.996250 and purity 0.99251875 throughout—consistent with those shared channel assumptions.
The research question
How do orbit-model choices change predicted geometry and timing when the initial state is held fixed? This study supports controlled model comparison and a reproducible starting point for further link investigations.
How to interpret it
The spacecraft supply example orbital geometry; they are not claimed to carry the modeled quantum equipment. These figures are a dated replay, not a live feed, measured optical performance or evidence of a PF advantage.
The installed PF application supports current-UTC tracking with periodically refreshed elements. This Gallery preserves the captured inputs so the displayed result can be reproduced.
06 / Qiskit Aer modeling
Change the noise.
Examine the encoding.
Compare singlet and Φ⁺ polarization states under the same declared Gaussian phase-noise model, then inspect how simulated finite-shot estimates relate to exact density matrices.
Ten sampled cases use nine Pauli settings with 8,192 shots per setting. The 210 checks concern exact-state fidelity, purity and physicality; finite-shot points are statistical estimates. The largest exact fidelity and purity reference discrepancies were 2.00 × 10⁻¹⁵ and 3.11 × 10⁻¹⁵.
The research question
Which encoding is less sensitive to the phase correlations in your apparatus? In this declared model, the singlet favors positively correlated noise, while Φ⁺ favors anticorrelated noise. A real design choice requires a calibrated noise model.
Keep the assumptions visible
The covariance is explicitly supplied; it is not inferred from satellite position, distance or a reference frame. Results are conditioned on collecting both photons. Loss and collection rates are calculated separately.
The bundle includes a function-level sweep driver and its configuration; it is not a GUI scenario preset. The run used Qiskit 2.5.2 / Aer 0.17.2. Optional Qiskit Experiments was audited separately and was not used to generate these figures. No quantum hardware was accessed.
07 / ISAES scientific analysis
Follow the quantum state.
Inspect the evidence.
Run a six-qubit driven spin chain, inspect its retained density matrices, then analyze a grid of executed configurations with four classical methods.
The full-register heatmap and the q0 checkpoints come from the same fresh eight-cycle reference run. The classical analysis uses a separate parameter grid of actual executions of that same Floquet model. The complete configuration, complex matrices, observables and numerical checks accompany the figures.
The complete six-qubit state
The final density matrix has 64 basis states on each axis. Color shows its real entries; the download also retains every imaginary component.
One qubit through the saved cycles
Trace out the other five qubits to inspect q0. Begin at cycle 3, then compare the initial state and every retained cycle.
After cycle 3 · saved checkpoint 4 of 9
- Purity
- 0.634318
- Population |0⟩
- 0.407038
- Population |1⟩
- 0.592962
- Coherence |ρ₀₁|
- 0.241903
Each selection displays a stored numerical state. The selector does not interpolate between cycles.
What does each state tell you?
The full matrix describes the complete register. The reduced matrix describes q0 alone. Its purity, populations and coherence help track local evolution; the reduced state does not retain all correlations between the six qubits.
Keep the calculation connected
Each displayed checkpoint is tied to its cycle, source configuration and retained numerical output. The study checks trace, Hermiticity, positivity and consistency with an independently implemented reference evolution.
Four views of the executed parameter grid
PCA and clustering summarize variation in the calculated observables. Density grouping identifies neighborhoods and noise under declared settings. Reference distances quantify separation from the chosen reference set. Held-out predictions estimate final-state purity on configuration groups excluded from fitting.
The four-panel image is a documented plotting composition of results computed with r34’s ISAES analyzers. It is not an automatic four-panel Workbench layout. Clusters and large reference distances are exploratory descriptions; they do not establish a physical phase or a hardware fault. Prediction results apply to the saved split and model.
These are numerical simulations and calculated analyses. No quantum hardware measurements are represented. The Gallery displays saved results; repeat the study in the PF research environment using the supplied driver and runtime requirements.
Reproducibility
Every figure has a starting point.
The Gallery contains six executed numerical studies: the gauge-wave-link study, HOM interference, channel tomography, satellite replay, the Aer encoding sweep and the ISAES Floquet study. The satellite study combines a two-hour orbit rendering with a separate matched 120-second comparison.
Use the original configurations for the first three studies. The satellite, Aer and ISAES Floquet bundles include their own reproduction instructions, saved numerical data and plotting drivers. Each method page states the model, input provenance and what was checked.
Independent inspection: The study bundles contain configurations, numerical outputs and reproduction instructions. Satellite, Aer and ISAES Floquet checks support their specified models and cases; full-platform and live-provider qualification are separate.