What we measured on IBM Heron r2 · ibm_fez. Same physics, two levels of detail, one public page. Job d6tfp1gv5rlc73f2qh5g.
We stored one logical bit per block on five physical qubits and ran eighteen such blocks in parallel (90 qubits) in one circuit. When we vote across the five (majority readout), we read the intended bit more reliably than when we trust only one qubit in that block, on the same machine, same run. That is architectural tolerance: the design of the readout.
Think of five sensors measuring the same yes/no signal. Taking the majority beats listening to one sensor alone. Here the sensors are qubits on IBM Heron r2 · ibm_fez; the signal is the logical 0/1 we encoded.
This is the QPC idea of multiple carriers (kenograms) for one logical degree of freedom: robust readout on the same hardware job.
Named job d6tfp1gv5rlc73f2qh5g: 18×5 = 90 qubits, 4096 shots. Typical ranges from sibling runs sit next to those exact figures.
| What we compare | Typical per-bit logical error* | In plain words |
|---|---|---|
| Majority (vote over 5 qubits per block) | 4.47% (typical ~4.3–4.7%) | About 1 in 22 logical bits disagree with the encoded value after decode. |
| Single qubit (read only the first qubit in each block) | 5.48% (typical ~5.5–6.5%) | About 1 in 18 logical bits disagree with the encoded value. |
* “Per-bit logical error” = fraction of block-decisions that disagree with the known encoded value, averaged over all blocks and shots.
Word-level metric: a word means all 18 blocks correct in one shot. That is a hard bar: one wrong block fails the word. On job d6tfp1gv5rlc73f2qh5g, word error is 61.23% (majority) vs 69.34% (single qubit). Majority beats single-qubit on the same data.
What this shows: QPC-style redundant encoding + majority readout improves logical readout versus a single-carrier baseline on the same IBM Heron r2 job.
Same machine, two readouts. Majority vs single-qubit on the same Fez circuit makes the architectural gain visible. Related structure-recovery work: Holographic Memory, Quantum-native task, and SWR executive results.
Cross-check from the structure line. The Fez SWR/CSI confirmation batch reports 7/7 runs above chance with mean cluster recovery 52.04% (95% CI 48.04–56.04%). Redundancy improves readout here; SWR/CSI tracks recoverable structure on the same fleet.
|0⟩^{⊗5} or X + proprietary coupling → |1⟩^{⊗5}
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Measure all 90 qubits
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Decode: majority vs first qubit only
logical_bits[b] per block (PRNG-seeded) for error accounting.opt_level=0 default), initial_layout from greedy disjoint paths.--fast (forward array concat + LSB-right block parsing) consistent with Fez.For each shot and each block b, compare decoded bit (majority or q0) to logical_bits[b]. Aggregate: errors / (shots × B).
Fraction of shots where any of the B blocks decodes incorrectly. Highly sensitive to B (product of per-block success probabilities).
On job d6tfp1gv5rlc73f2qh5g the per-bit gap is 1.01 percentage points (majority 4.47% vs single 5.48%). Majority is a classical five-copy vote on Z-basis outcomes. That margin is the redundancy result on IBM Heron r2.
Reproducibility: Script qpc_redundant_kenogram_ibm.py. Outputs: qpc_redundant_kenogram_ibm.json.
| Kenogram block | Five physical qubits carrying one logical bit via repetition-style preparation. |
|---|---|
| Majority readout | Per shot, logical bit = majority of the five measured bits in that block. |
| Single-qubit baseline | Same measurement string; logical bit = first qubit of the path only. Fair control. |
| Graceful degradation | Better logical fidelity from redundancy + decode on the same hardware job, same gate error ε. |