What we measured on real hardware (IBM Fez), in language for customers and quantum researchers. Same physics, two levels of detail.
We stored one logical bit per “block” on five physical qubits and ran eighteen such blocks in parallel (90 qubits). 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, not a claim that the processor magically got quieter.
Think of five sensors measuring the same yes/no signal. If each sensor is a bit noisy, taking the majority usually beats listening to one sensor alone. Here the “sensors” are quantum bits on IBM’s Fez chip; the “signal” is the logical 0/1 we encoded.
This aligns with the QPC idea of multiple carriers (kenograms) for one logical degree of freedom—useful when you care about robust readout as devices mature, not only about raw single-qubit fidelity.
Exact figures vary slightly per job (calibration, queue). Below are typical ranges from completed jobs with 18×5 qubits, 4096 shots.
| What we compare | Typical per-bit logical error* | In plain words |
|---|---|---|
| Majority (vote over 5 qubits per block) | ~4.3–4.7% | About 1 in 22 logical bits wrong after decode. |
| Single qubit (read only the first qubit in each block) | ~5.5–6.5% | About 1 in 17–18 logical bits wrong. |
* “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” here means all 18 blocks correct in one shot. That bar is harsh: even ~5% error per block makes full success rare (~0.9518 ≈ 40% best case). So word error rates in the 60–80% range are expected; what matters for the story is that majority consistently beats single-qubit on the same data.
What we do not claim: We are not claiming to beat every classical post-processing method, or full quantum error correction. We show that QPC-style redundant encoding + majority readout improves logical readout versus a single-carrier baseline on NISQ hardware.
NISQ across QPC demos. Like other QPC hardware tests, this one is bounded by universal device noise and depth, not by a special “QPC penalty.” We compare majority vs single-qubit readout on the same machine so the architectural gain is visible despite noise. For the same framing on holographic and structure-recovery work, see Holographic Memory, Quantum-native task, and SWR executive results.
Cross-check from the structure line. The latest Fez SWR/CSI confirmation batch reports 7/7 runs above chance with mean cluster recovery 52.04% (95% CI 48.04–56.04%) in a structure-focused decoder setting. This is a complementary signal: redundancy improves readout fidelity here, while SWR/CSI tracks recoverable structure under the same NISQ reality.
|0⟩^{⊗5} or X + CNOT chain → |1⟩^{⊗5}
→
Measure all 90 qubits
→
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).
The ~1–2 percentage-point gap in per-bit error (majority vs single) is consistent with independent-ish readout/gate noise on five copies—majority is a classical [[5,1,3]]-style repetition decode on Z-basis outcomes (not a full QEC code on the device). Correlated noise across the chain would reduce the margin; we still observe a clear improvement, which is informative for NISQ redundancy studies.
Reproducibility: Scripts qpc_redundant_kenogram_ibm.py (--fast --quiet for minimal pipeline), local MC baseline qpc_redundant_kenogram_demo.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, without claiming lower intrinsic gate error (ε). |