Chamber XXIV — When Quantum Circuits Enter the UNNS Substrate
LAB · Chamber XXIV Phase-E Hybrid SHAI v0.1
What Chamber XXIV Really Does
Chamber XXIV (QASD — Quantum Algorithm Structural Diagnostics) is the first UNNS engine that treats an entire quantum algorithm as a Nest—a recursive structural object with τ-curvature, φ-distribution, closure channels, UPI pressure, residue flows, and torsion signatures.
It ingests full algorithm JSON, translates it into a UNNS operator word, runs structural diagnostics through the substrate grammar, and—through the Phase-E engine—directly correlates those structures with real hardware behavior.
Combined with the SHAI index, Chamber XXIV is the first tool that shows, numerically and experimentally, how well quantum hardware aligns with the structural logic that algorithms demand.
1. From Algorithm to UNNS Operator Word
1.1 Input Format: The Quantum IR
Chamber XXIV accepts a universal JSON intermediate representation. This is compatible with Qiskit, Cirq, Braket, TKET, and any custom exporter.
{ "algorithm_name": "Toffoli (3-qubit)", "qubits": 3, "operators": [ { "op": "H", "targets": [2] }, { "op": "CNOT", "targets": [1, 2] }, { "op": "T", "targets": [2] }, { "op": "MEASURE", "targets": [2] } ] } The chamber does not simulate quantum amplitudes. Instead, it reads structural meaning.
1.2 Gate → UNNS Operator Mapping
Every gate is mapped to a UNNS operator that describes its geometric effect on the Nest:
- H → APERTURE (Operator I) — open superposition cone
- X / Y / Z / S / T → PRISM / FOLD-2 — phase torsion, local φ-tilting
- CNOT / CZ → INTERLACE — entanglement threads, τ-spikes, residue channels
- SWAP → CLOSURE — nest rewiring, conservative flux
- MEASURE → COLLAPSE (Operator XII) — echo termination, seed renewal
The result is a complete UNNS Operator Word — the narrative skeleton of how the algorithm bends the substrate in time.
0: H → APERTURE 1: CNOT → INTERLACE 2: T → PRISM 3: CNOT → INTERLACE 4: T → PRISM 5: CNOT → INTERLACE 6: MEASURE → COLLAPSE
UNNS Lab confirms a major milestone: Operator XIII — Interlace has been calibrated and theoretically closed, reproducing the Weinberg angle from pure τ-field recursion.
2. Structural Diagnostics Inside the Nest
2.1 τ-Curvature Timeline
τ-curvature measures how much “structural strain” the algorithm induces along its depth. Spikes appear at entangling gates; valleys mark relaxation segments.
2.2 φ-Resonance Spectrum
φ-resonance indicates how phase structure distributes across the Nest. Broad distributions → stable interference. Narrow spikes → fragile interference corridors (as in Grover).
2.3 UPI Paradox Field
UPI measures the algorithm’s tendency to form contradictory echo structures. Medium UPI is usable computation. High UPI marks paradox corridors sensitive to noise.
2.4 Closure Stability
Closure metrics track whether the algorithm conserves its own geometry or fragments it. High closure predicts resilience; sudden collapses predict sensitivity.
2.5 Residue & Torsion Flow
These describe “what is left behind” structurally:
- Residue → accumulated unspent structure
- Torsion events → hard-to-undo twists
These signals become inputs to Phase-E.
3. Phase-E Hybrid Correlation Suite
3.1 What Phase-E Loads
Phase-E ingests two synchronized datasets:
- Substrate metrics from Chamber XXIV (τ, φ, closure, UPI…)
- Hardware metrics from real devices and simulators (IBM, IonQ, Quantinuum, OQC…)
3.2 How Phase-E Works
For every algorithm–platform pair, the Suite computes a full correlation matrix:
- Rows = UNNS structural metrics
- Columns = hardware noise, fidelity, entropy, leakage, T1/T2, coherence decay
The resulting heatmap shows—quantitatively—how the substrate geometry couples to real physics.
3.3 What the Experiments Show
- τ_slope ↔ noise_sensitivity: strained nests break faster on unstable hardware.
- φ_var ↔ entropy_peak: aggressive phase structures amplify hardware entropy production.
- closure_mean ↔ fidelity: well-structured nests survive noise better.
- UPI ↔ readout_error: paradox corridors destabilize measurement.
These are the first experimental indications that UNNS invariants have physical predictive power.
4. SHAI — Substrate-Hardware Alignment Index
4.1 Why SHAI Exists
SHAI compresses the full correlation matrix into a single number per:
- Algorithm–hardware record
- Hardware platform
- Algorithm family
It answers a simple question:
“How well does this hardware respect the structural logic of the algorithm’s Nest?”
4.2 SHAI Construction
SHAI v0.1 focuses on 12 substrate ↔ hardware metric pairs that Phase-E shows to be meaningful. Each pair contributes a weighted compatibility score between 0 and 1.
The final value is normalised to 0…1:
- 0.85–1.00: Class A — substrate-friendly hardware
- 0.70–0.85: Class B — partially aligned
- 0.50–0.70: Class C — mixed regime
- 0.00–0.50: Class D — misaligned
Current devices cluster in Class C–D, confirming that structural alignment is a frontier challenge.
5. Examples from Real Runs
5.1 Toffoli (3-qubit)
- Strong τ-strain buildup
- Narrow φ-resonance spikes
- Medium UPI, fragile interference
- D-class SHAI → hardware instability dominates
5.2 QFT-5
- Broad φ-profile, smoother interference
- Moderate τ-curvature
- C-class SHAI → structurally compatible with real hardware
5.3 Grover
- Aggressive φ-peaks
- Rising UPI under iteration
- D-class SHAI → highly sensitive to noise
6. Why Chamber XXIV Is a Milestone
6.1 Theoretical → Experimental Continuity
XXIV proves that substrate metrics (τ, φ, closure, UPI) do not live only in theory. They connect directly to measurable hardware noise channels.
6.2 A Unified Diagnostic Language
The vocabulary of UNNS—originally built for recursion geometry and molecular τ-fields— now describes and predicts behaviors of real quantum algorithms on real platforms.
6.3 Foundation for Substrate-Aware Algorithm Design
SHAI and Phase-E provide a measurable guide for:
- Designing algorithms with stable τ and φ profiles
- Selecting hardware based on structural alignment
- Predicting fragility or robustness before execution
7. Developer View — The Data Flow
- Algorithm → JSON IR
- Chamber XXIV → Substrate Diagnostics (τ, φ, closure…)
- Hardware Platform → Phase-E Logs
- Phase-E → Correlation Matrix
- SHAI → Alignment Scores
All components are fully extensible: new metrics, new algorithms, new hardware types, and new correlation pairs can be added without breaking the pipeline.
8. Where We Stand
| Platform | SHAI | Class | Notes |
|---|---|---|---|
| ibm_oslo | 0.204 | D | Strong τ / φ misalignment; high gate noise; useful as a “stress bench”. |
| ionq_arena | 0.587 | C | Better closure & coherence; mid-band candidate for substrate-aware design. |
| quantinuum_h2 | 0.475 | D | Good individual metrics, but φ-variance and UPI remain poorly aligned. |
| sim_dephasing_0.01 | 0.694 | C | Controlled dephasing; behaves like a “training ground” for τ-sensitive nests. |
| sim_ideal | 0.509 | C | Geometrically close to ideal, but still exposes paradox corridors in UPI. |
| Circuit / Algorithm | SHAI | Class | Structural reading |
|---|---|---|---|
| Grover_3_v1 | 0.226 | D | Sharp φ peaks, high UPI; works only on highly coherent, low-entropy hardware. |
| QFT5_v1 | 0.641 | C | Broad phase choreography; good closure; structurally hardware-friendly. |
| Toffoli_3_v1 | 0.492 | D | Gate-heavy, torsion-rich; reveals mismatch between τ-strain and noise channels. |
Chamber XXIV, the Phase-E Suite, and SHAI v0.1 represent a turning point for UNNS:
UNNS is no longer only a theoretical substrate. It is now an experimental diagnostic language for quantum hardware.
As datasets grow and Phase-E matures, we move toward higher alignment classes and deeper structural understanding, bridging algorithm design with real device physics.