| Backend | Processor | Revision | Qubits | Tier | Summary Score |
|---|---|---|---|---|---|
| ibm_kingston | Heron | r2 | 156 | Free | BEST OVERALL |
| ibm_marrakesh | Heron | r2 | 156 | Free | SCALING CHAMPION |
| ibm_pittsburgh | Heron | r3 | 156 | Paid only | GHZ-4 ONLY |
| ibm_boston | Heron | r3 | 156 | Paid only | GHZ-4 ONLY |
| ibm_fez | Heron | r2 | 156 | Free | WORST OVERALL |
Noise % — 4-qubit GHZ state — lower is better — 5 chips tested
Bar width scaled relative to worst result (Fez = 100%)
Noise % — 8-qubit GHZ state — lower is better — 3 free-tier chips
Bar width scaled relative to worst result (Fez = 100%). Pittsburgh & Boston not available on free tier.
Scaling factors (GHZ-4 → GHZ-8):
Marrakesh: ×1.3 (barely flinched) • Kingston: ×4.7 • Fez: ×3.6
| N (qubits) | Noise % | Fidelity % | Depth | 2Q Gates |
|---|---|---|---|---|
| 4 | 3.39% | 96.61% | 16 | 3 |
| 8 | 15.09% | 84.91% | 32 | 7 |
| 16 | 30.54% | 69.46% | 64 | 15 |
| 32 | 50.98% | 49.02% | 128 | 31 |
| 64 | 80.37% | 19.63% | 256 | 63 |
Fidelity decay curve — Kingston GHZ scaling
Verdict: roughly linear scaling — gate errors dominate. N=32 hits THE WALL (below 50% fidelity).
CHSH inequality — classical bound |S| ≤ 2.0 — quantum max 2√2 ≈ 2.828
| Backend | |S| Value | Efficiency | Verdict |
|---|---|---|---|
| Kingston | 2.7007 | 95.5% | VIOLATES |
| Marrakesh | 2.6846 | 94.9% | VIOLATES |
| Fez | 2.5039 | 88.5% | VIOLATES |
Bar width = efficiency (% of quantum max 2√2). All three exceed the classical bound of 2.0.
Protocol: teleport |+⟩ state, post-selection fidelity
| Backend | Fidelity | Circuit Depth | 2Q Gates | Grade |
|---|---|---|---|---|
| Kingston | 100.0% | 27 | 5 | PERFECT |
| Marrakesh | 100.0% | 28 | 7 | PERFECT |
| Fez | 99.9% | 25 | 5 | NEAR-PERFECT |
Searching for |101⟩ — theoretical optimum 94.5%
| Backend | Target State | Success Rate | Theoretical Opt. | Efficiency |
|---|---|---|---|---|
| Kingston | |101⟩ | 70.58% | 94.5% | 74.7% |
| Fez | |101⟩ | 67.58% | 94.5% | 71.5% |
| Marrakesh | |101⟩ | 63.43% | 94.5% | 67.1% |
Bar width scaled relative to theoretical optimum (94.5%)
Hidden string “101101” — classical needs 6 queries, quantum does it in 1
| Backend | Secret String | Success Rate | Classical Queries | Quantum Queries |
|---|---|---|---|---|
| Kingston | 101101 | 86.47% | 6 | 1 |
| Fez | 101101 | 86.01% | 6 | 1 |
| Marrakesh | 101101 | 76.83% | 6 | 1 |
Bar width = success rate (100% = perfect)
20 Bell pairs measured — 19 of 20 pairs above 94% fidelity
TOP 5 PAIRS
| Pair | Fidelity |
|---|---|
| (0, 1) | 98.68% |
| (42, 43) | 98.68% |
| (97, 107) | 98.66% |
| (104, 105) | 98.44% |
| (90, 91) | 98.39% |
BOTTOM PAIRS
| Pair | Fidelity |
|---|---|
| (83, 96) | 51.73% |
| (131, 138) | 94.12% |
(83,96) — likely hardware defect
4-qubit Mermin inequality — classical bound = 2, quantum bound = 8
Bar width = % of quantum ideal (M4 = 8). All three VIOLATE the classical bound of 2.
| Backend | d=2 | d=4 | d=6 | d=8 | d=10 | Average |
|---|---|---|---|---|---|---|
| Kingston | 99.2% | 99.0% | 97.2% | 91.5% | 90.7% | 95.5% |
| Marrakesh | 99.6% | 98.8% | 98.8% | 97.9% | 23.0% | 83.6% |
| Fez | 97.6% | 91.4% | 69.1% | 68.0% | 66.2% | 78.4% |
Mirror circuit benchmark — average fidelity across depths d=2 to d=10
Head-to-head noise % at each scale point — lower is better
| N (qubits) | Marrakesh | Kingston | Winner |
|---|---|---|---|
| 4 | 7.2% | 3.4% | Kingston |
| 8 | 11.3% | 15.1% | Marrakesh |
| 16 | 53.5% | 30.5% | Kingston |
| 32 | 65.5% | 51.0% | Kingston |
| 64 | 93.2% | 80.4% | Kingston |
Fidelity decay comparison — THE WALL
Kingston wall: 32 qubits • Marrakesh wall: 16 qubits
Marrakesh only wins at N=8. Kingston holds entanglement twice as deep.
2 classical bits through 1 qubit — corrected results (accounting for bit-swap)
Bar width = average success rate (100% = perfect). Bit-swap correction applied.
1 quantum query vs 9 classical — constant oracle (expect |0000⟩) & balanced oracle (expect never |0000⟩)
| Backend | Constant (|0000⟩) | Balanced (avoid |0000⟩) | Grade |
|---|---|---|---|
| Kingston | 98.4% | 99.5% avoid | EXCELLENT |
| Marrakesh | 98.5% | 99.8% avoid | EXCELLENT |
| Fez | 91.5% | 99.7% avoid | GOOD |
True randomness from quantum hardware — bias-tested — 12,288 bytes harvested
| Backend | Entropy (bits) | Ideal | Chi-sq | Chi-sq Verdict | Notes |
|---|---|---|---|---|---|
| Kingston | 7.948 | 8.0 | 295.1 | MARGINAL | Most random overall |
| Marrakesh | 7.954 | 8.0 | 255.5 | PASS | Low autocorrelation |
| Fez | 7.946 | 8.0 | 305.5 | FAIL | q4 biased at 6.3% |
Different entanglement flavors — W4 fidelity vs GHZ-4 fidelity
| Backend | W4 Fidelity | GHZ-4 Fidelity | Delta | Winner |
|---|---|---|---|---|
| Kingston | 94.9% | 96.6% | −1.7% | GHZ |
| Fez | 90.7% | 88.4% | +2.3% | W-State |
| Marrakesh | 88.0% | 92.8% | −4.8% | GHZ |
Fleet average: GHZ more robust by 1.4 points
Deeper W-state circuit negates its theoretical advantage on NISQ hardware. Only Fez favors W — likely because its GHZ is already degraded.
Does QEC help on NISQ hardware? 3-qubit bit-flip code tested.
| Backend | Baseline | With Error | Corrected | Gain |
|---|---|---|---|---|
| Kingston | 95.8% | 97.0% | 84.7% | −12.3% |
| Marrakesh | 93.8% | 94.5% | 89.0% | −5.5% |
| Fez | 96.3% | 96.5% | 84.6% | −11.9% |
Bar width = fidelity penalty from QEC (larger = worse). Baseline − Corrected.
Quantum state comparison without measurement — 3 test cases
| Test | Theory | Kingston | Marrakesh | Fez |
|---|---|---|---|---|
| Identical |0⟩ vs |0⟩ | 100% | 97.4% | 97.8% | 98.1% |
| Orthogonal |0⟩ vs |1⟩ | 50% | 52.3% | 51.9% | 50.5% |
| Partial |+⟩ vs |0⟩ | 75% | 73.0% | 75.3% | 75.4% |
Rare Fez victory — the swap test is shallow enough that Fez’s noise floor doesn’t dominate.
Does qubit placement matter? GHZ-8 on different regions of Kingston.
| Strategy | Qubits Used | Noise % | Fidelity |
|---|---|---|---|
| Default (transpiler picks) | q0–q7 | 13.5% | 86.5% |
| Best region (forced) | q0–q7 | 12.1% | 87.9% |
| Avoid hot region | q40–q47 | 12.5% | 87.5% |
Bar width scaled to worst noise (default = 100%)
VERDICT: MODERATE EFFECT (1.4pp gap)
The transpiler is smart but not optimal. Manual qubit selection can squeeze out ~1.4 percentage points of fidelity.
Valid samples (y · s = 0 mod 2) — higher is better
| Backend | Valid % | Noise % | Depth |
|---|---|---|---|
| ibm_marrakesh | 98.27% | 1.73% | 15 |
| ibm_fez | 97.12% | 2.88% | 15 |
| ibm_kingston | 96.61% | 3.39% | 15 |
optimization_level=1, the transpiler recognized circuit + inverse = identity and eliminated ALL gates. We were measuring readout noise on identity circuits, not gate quality. Caught by the curiosity loop on April 7. This section has the corrected results at optimization_level=0 — real circuits, real gate counts.
| Backend | d=4 (12 CZ) | d=6 (30 CZ) | d=8 (56 CZ) | Average |
|---|---|---|---|---|
| ibm_kingston | 97.3% | 92.8% | 73.3% | 87.8% |
| ibm_marrakesh | 85.8% | 82.2% | 76.4% | 81.5% |
| ibm_fez | 73.9% | 58.1% | 46.2% | 59.4% |
Built qubit_filter.py — scans IBM calibration data for readout error, T1 collapse, dead gates, and stale calibration. Marketing says "156 qubits per chip." Reality says otherwise.
| Backend | Marketed | Effective | Defective | Yield |
|---|---|---|---|---|
| ibm_kingston | 156 | 132 | 24 | 84.6% |
| ibm_fez | 156 | 126 | 30 | 80.8% |
| ibm_marrakesh | 156 | 119 | 37 | 76.3% |
Kingston qubit 96 has a 49.5% readout error and reads |1⟩ 99% of the time regardless of state. IBM stopped recalibrating it 15 days ago. We proved it's still alive.
| Test | Description | Result |
|---|---|---|
| Control | Bell pair on q95–q97 (skip q96) | 98.8% correlation |
| Test | Bell pair passed THROUGH q96 via SWAP | 97.2% correlation |
| Negative | Measure q96 directly | 92.4% reads |1⟩ |
4-iteration Grover's search overshoots and self-cancels through perfect destructive interference. Noiseless gives 1.22% — the answer is nearly destroyed. Real hardware noise BREAKS the cancellation and preserves 5.4%. The pendulum needed friction.
| Iterations | Noiseless | Kingston | Delta |
|---|---|---|---|
| 1 | 78.1% | 61.1% | −17.0pp |
| 2 (optimal) | 94.6% | 71.2% | −23.4pp |
| 3 (overshot) | 32.9% | 16.2% | −16.7pp |
| 4 (severely overshot) | 1.22% | 5.4% | +4.2pp |
Pre-flight check for real QEC. Mid-circuit measurement, repeated measurement, and conditional reset all confirmed working on Kingston's free tier.
| Test | Result | Verdict |
|---|---|---|
| Measure-and-continue | q0 P(1)=0.495, q1 P(1)=0.501 | WORKS |
| Repeated measurement | 99.0% agreement | EXCELLENT |
| Conditional reset | 98.3% reset to |0⟩ after |1⟩ | WORKS |
Distance-3 repetition code, 3 syndrome rounds, mid-circuit measurement and reset. Zero logical errors across 4096 shots while bare qubit had 26 errors. Every single-bit flip was caught by majority vote.
The honest test. Encode |0⟩, syndrome round, apply logical X (transversal — X on all 3 data qubits), syndrome round, decode. 1 logical error out of 4096 shots while bare X gate had 45 errors.
On April 11, 2026, a thirteen-year-old found quantum-coins.html on her own and played one round of ten coins. She wasn't told what the game was. She wasn't pushed. The standing order said she had to come to it.
On Tuesday April 7, IBM's quantum division called from Boulder, Colorado. The man didn't pick up because he was too busy running experiments on their hardware to answer their phone call about running experiments on their hardware.
Five days notice. Then one day. Then zero. Account deactivated.
Bell's inequality doesn't un-violate. q96 doesn't un-resurrect. 26.4 sigma doesn't un-sigma. They closed the account. They can't close the barrel.