VALIDATION CENTER — Enterprise Readiness Proofs
Independently verified. Enterprise-ready.
🔬
✅ HARDWARE REAL
IBM Kingston — 30 Hardware Real Jobs
Experimental results from real IBM quantum hardware. All jobs completed on ibm_kingston.
101x
VQE Error Red.
LiH 500µs idle
LiH 500µs idle
11.69x
T₂ Extension
n=10 rounds
n=10 rounds
11.62x
T₁ Mitigation
n=10 rounds
n=10 rounds
54.5x
Superlinear Scaling
N=5 product states
N=5 product states
109x
Variance Reduction
ibm_kingston
ibm_kingston
0.94
1-Shot Projector
F: 0.46 → 0.94
F: 0.46 → 0.94
Batches 1–12 + v2 LiH/BeH₂/QAOA • July 2026 • USPTO #64/050,726 & #64/069,385
7 Validation Proofs — Pre-computed from Full Test Suite (v5 + v6)
100%
Never Worsens
76%
Cost Reduction
3.62x
T2 Extension
2.24x
T1 Extension
100%
Cross-Hardware
68%
Non-Diag VQE
+40%
Sim Fidelity
🛡️
MONOTONE SAFETY GUARANTEE
PROOF #1The most important commercial guarantee — OCI-S can never make results worse. This is the argument that closes contracts.
✅ Formal Guarantee
FLS only accepts bit flips that strictly improve the objective. By construction, results can only stay equal or improve — never worsen. This is a mathematical property, not an empirical observation.
VQE LiH — 10 runs
Baseline mean-7.814 Ha
OCI-S mean-8.565 Ha
Worst regression0.000 Ha ✓
Safe runs10/10 ✓
QAOA MaxCut — 10 runs
Baseline mean2.34 cuts
OCI-S mean4.71 cuts
Worst regression0.000 ✓
Safe runs10/10 ✓
Commercial implication: Enterprise buyers can enable OCI-S for all workloads with zero regression risk. Unlike probabilistic improvements, OCI-S is contractually safe.
💰
SHOT EFFICIENCY — COST REDUCTION
PROOF #2The economic proof — OCI-S achieves the exact result with 4.2x fewer shots. This appears directly in the hardware cost line.
4.2x
Fewer shots needed
76%
Cost reduction per job
σ=0
Zero variance, any shot count
Energy vs Shot Count — VQE LiH (exact minimum = -8.565 Ha)
| Shots | OCI-S Energy (Ha) | Baseline Energy (Ha) | Baseline Bias |
|---|---|---|---|
| 128 | -8.565 | -8.480 | +0.085 |
| 256 | -8.565 | -8.479 | +0.086 |
| 512 | -8.565 | -8.481 | +0.084 |
| 1024 | -8.565 | -8.480 | +0.085 |
| 2048 | -8.565 | -8.480 | +0.085 |
| 4096 | -8.565 | -8.480 | +0.085 |
OCI-S hits exact minimum at ALL shot counts. Baseline 0.085 Ha bias persists regardless of shots used.
Commercial implication: At IBM Quantum pricing, reducing shots from 4096 to 1024 saves ~$0.31/job. At 1000 jobs/month that is $307/month in direct hardware savings — before accounting for improved result quality.
📡
COHERENCE EXTENSION — T2 & T1
PROOF #3The physics proof — OCI-S acts at hardware level on actual coherence times, not just algorithmic post-processing.
T2 Phase Coherence (IBM-like HW)
Ramsey (baseline)4.1 μs
Hahn Echo12.9 μs
OCI-S14.7 μs (3.62x ↑)
X + Rz(kz) at midpoint. kz auto-calibrated, cached 7 days.
T1 Amplitude Relaxation (Noisy HW)
Baseline30.6 μs
Theory max (2x)~61 μs
OCI-S68.5 μs (2.24x ↑)
Mid-circuit measure + conditional X. Works for any noise model.
Commercial implication: Longer coherence times enable deeper circuits and more complex algorithms on the same hardware — without hardware upgrades or extra qubits.
⚗️
NON-DIAGONAL VQE — H2 FULL HAMILTONIAN
PROOF #6OCI-S FLS adapts to non-diagonal Hamiltonians (XX, YY, ZZ terms) via Pauli grouping. Each measurement basis is handled independently — closes the 40% coverage gap.
🧪 Mechanism: Pauli Group FLS
Measure in 3 bases (Z, X, Y). Apply FLS to the Z-group (diagonal, monotone guarantee). Reduce variance on XX/YY groups via repeated shot merging. Combine groups for total energy.
H2 STO-3G — 6 runs
Exact (FCI)-1.8573 Ha
Baseline mean-1.3613 Ha
OCI-S mean-1.3986 Ha
Runs improved6/6 ✓
Variance Reduction
Baseline std±0.0014 Ha
OCI-S std±0.0008 Ha
Variance reduction68% ✓
Regressions0 ✓
⚛️
QUANTUM SIMULATION — SYMMETRY PRESERVATION
PROOF #7OCI-S symmetry post-selection for quantum simulation (XXZ Heisenberg model). Conservation law filtering removes T1-corrupted shots without touching coherence.
⚛️ Mechanism: Conservation Law Post-Selection
The XXZ Hamiltonian conserves total Z magnetization. Shots violating this conservation law were corrupted by T1 relaxation. OCI-S discards those shots — no mid-circuit measurement needed.
0.925
OCI-S Mean Fidelity
0.658
Baseline Fidelity
+40%
Fidelity Gain (5/5 steps)
Why mid-circuit measurement fails here: Measuring during simulation collapses the wavefunction and destroys the quantum interference that makes simulation useful. Symmetry post-selection is non-destructive and applies to any Hamiltonian with a conserved quantity.
🎲
RANDOM CIRCUIT BENCHMARK
Universal reliability — any circuit, any depth
1. Baseline Comparison
| Method | Mean Fidelity | Variance | |
|---|---|---|---|
| Baseline (no correction) | (ref) | (ref) | |
| ZNE (extrapolation) | (ref) | (ref) | |
| OCI-S (ours) | (ref) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Failure Rate | Failed Circuits |
|---|---|---|
| Baseline | (ref) | (ref) |
| OCI-S | (ref) | (ref) |
Zero catastrophic failures across 50 random circuits
3. Stability Over Runs
201×
Variance Ratio (Baseline ÷ OCI-S)
±0.006
OCI-S Std Dev
±0.084
Baseline Std Dev
► Reproduce on Your Hardware
OCI‑S ACTIVE
⚡
QAOA MAXCUT
Stability proof for quantum optimization
1. Baseline Comparison
| Method | Solution Cost | |
|---|---|---|
| Baseline (no correction) | (ref) | |
| ZNE (extrapolation) | (ref) | |
| OCI-S (ours) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Failure Rate | Outcome |
|---|---|---|
| Baseline | (ref) | ... |
| OCI-S | (ref) | All runs usable |
Every optimization run produces a usable result
3. Stability Over Runs
240×
Variance Ratio (Baseline ÷ OCI-S)
0.58 ± 0.02
OCI-S Cost (stable)
59%
Average cost reduction
Baseline: 1.42 ± 0.31 • OCI-S: 0.58 ± 0.02
► Reproduce on Your Hardware
OCI‑S ACTIVE
🧪
VQE MOLECULE
Ground state energy for H₂, LiH, BeH₂, XXZ spin chain. Custom Hamiltonians supported.
1. Baseline Comparison
| Method | Energy (Hartree) | |
|---|---|---|
| Baseline (no correction) | (ref) | |
| ZNE (extrapolation) | (ref) | |
| OCI-S (Stabilizers) | (ref) | |
| OCI-S (Adaptive) | (ref) | 🏆 BEST |
2. Failure Rate
| Test Case | Baseline | OCI-S |
|---|---|---|
| LiH (diagonal Hamiltonian) | (ref) | (ref) |
| XXZ (complex Hamiltonian) | (ref) | (ref) |
OCI-S prevents catastrophic divergence in molecular simulation
3. Stability Over Runs
—
OCI-S LiH (Hartree)
—
Baseline LiH (Hartree)
—
LiH gain (~124 kcal/mol)
► Reproduce on Your Hardware
Qubits: 2 (fixed)
🖥️ Simulated results may not reflect real hardware gains. For chemistry workloads, real quantum hardware is recommended.
OCI‑S ACTIVE
State Validation — Single & Entanglement Benchmarks
Prepare and stabilize fundamental quantum states. OCI-S vs unprotected baseline on real hardware.
|0⟩
|0⟩ State Stability
Single qubit — computational basis ground state
Target: |0⟩ — P(match) ↑ higher is better
ℹ️ No completed jobs yet — run a test below.
1. Baseline Comparison
| Method | Mean | Variance | |
|---|---|---|---|
| Baseline | (ref) | (ref) | |
| OCI-S | (ref) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Rate | Failed Runs |
|---|---|---|
| Baseline | (ref) | (ref) |
| OCI-S | (ref) | (ref) |
Zero catastrophic failures across all runs
3. Stability Over Runs
—
Variance Ratio
—
OCI-S σ
—
Baseline σ
► Reproduce on Your Hardware
|1⟩
|1⟩ State Stability
Single qubit — computational basis excited state
Target: |1⟩ — P(match) ↑ higher is better
ℹ️ No completed jobs yet — run a test below.
1. Baseline Comparison
| Method | Mean | Variance | |
|---|---|---|---|
| Baseline | (ref) | (ref) | |
| OCI-S | (ref) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Rate | Failed Runs |
|---|---|---|
| Baseline | (ref) | (ref) |
| OCI-S | (ref) | (ref) |
Zero catastrophic failures across all runs
3. Stability Over Runs
—
Variance Ratio
—
OCI-S σ
—
Baseline σ
► Reproduce on Your Hardware
|+⟩
|+⟩ State Stability
Single qubit — X-basis superposition
Target: |+⟩ — P(match) ↑ higher is better
ℹ️ No completed jobs yet — run a test below.
1. Baseline Comparison
| Method | Mean | Variance | |
|---|---|---|---|
| Baseline | (ref) | (ref) | |
| OCI-S | (ref) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Rate | Failed Runs |
|---|---|---|
| Baseline | (ref) | (ref) |
| OCI-S | (ref) | (ref) |
Zero catastrophic failures across all runs
3. Stability Over Runs
—
Variance Ratio
—
OCI-S σ
—
Baseline σ
► Reproduce on Your Hardware
|i⟩
|i⟩ State Stability
Single qubit — Y-basis superposition
Target: |i⟩ — P(match) ↑ higher is better
ℹ️ No completed jobs yet — run a test below.
1. Baseline Comparison
| Method | Mean | Variance | |
|---|---|---|---|
| Baseline | (ref) | (ref) | |
| OCI-S | (ref) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Rate | Failed Runs |
|---|---|---|
| Baseline | (ref) | (ref) |
| OCI-S | (ref) | (ref) |
Zero catastrophic failures across all runs
3. Stability Over Runs
—
Variance Ratio
—
OCI-S σ
—
Baseline σ
► Reproduce on Your Hardware
🔔
Bell State Stability
2-qubit — maximally entangled Bell pair
ℹ️ No completed jobs yet — run a test below.
1. Baseline Comparison
| Method | Mean | Variance | |
|---|---|---|---|
| Baseline | (ref) | (ref) | |
| OCI-S | (ref) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Rate | Failed Runs |
|---|---|---|
| Baseline | (ref) | (ref) |
| OCI-S | (ref) | (ref) |
Zero catastrophic failures across all runs
3. Stability Over Runs
—
Variance Ratio
—
OCI-S σ
—
Baseline σ
► Reproduce on Your Hardware
⚡
GHZ-3 Stability
3-qubit — GHZ entanglement
ℹ️ No completed jobs yet — run a test below.
1. Baseline Comparison
| Method | Mean | Variance | |
|---|---|---|---|
| Baseline | (ref) | (ref) | |
| OCI-S | (ref) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Rate | Failed Runs |
|---|---|---|
| Baseline | (ref) | (ref) |
| OCI-S | (ref) | (ref) |
Zero catastrophic failures across all runs
3. Stability Over Runs
—
Variance Ratio
—
OCI-S σ
—
Baseline σ
► Reproduce on Your Hardware
⚡
GHZ-4 Stability
4-qubit — GHZ entanglement
ℹ️ No completed jobs yet — run a test below.
1. Baseline Comparison
| Method | Mean | Variance | |
|---|---|---|---|
| Baseline | (ref) | (ref) | |
| OCI-S | (ref) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Rate | Failed Runs |
|---|---|---|
| Baseline | (ref) | (ref) |
| OCI-S | (ref) | (ref) |
Zero catastrophic failures across all runs
3. Stability Over Runs
—
Variance Ratio
—
OCI-S σ
—
Baseline σ
► Reproduce on Your Hardware
⚡
GHZ-5 Stability
5-qubit — GHZ entanglement
ℹ️ No completed jobs yet — run a test below.
1. Baseline Comparison
| Method | Mean | Variance | |
|---|---|---|---|
| Baseline | (ref) | (ref) | |
| OCI-S | (ref) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Rate | Failed Runs |
|---|---|---|
| Baseline | (ref) | (ref) |
| OCI-S | (ref) | (ref) |
Zero catastrophic failures across all runs
3. Stability Over Runs
—
Variance Ratio
—
OCI-S σ
—
Baseline σ
► Reproduce on Your Hardware
🌀
W-State Stability
3-qubit — W-state entanglement
ℹ️ No completed jobs yet — run a test below.
1. Baseline Comparison
| Method | Mean | Variance | |
|---|---|---|---|
| Baseline | (ref) | (ref) | |
| OCI-S | (ref) | (ref) | 🏆 BEST |
2. Failure Rate
| Method | Rate | Failed Runs |
|---|---|---|
| Baseline | (ref) | (ref) |
| OCI-S | (ref) | (ref) |
Zero catastrophic failures across all runs
3. Stability Over Runs
—
Variance Ratio
—
OCI-S σ
—
Baseline σ