The ledger
Measured, on record.
A three-basis logical Bell fidelity with a confidence interval, 62 simultaneously-certified detection-code logical qubits, one-basis logical memory with real decoding, and a two-basis surface-code measurement quantifying the heavy-hex connectivity tax — all obtained on rented commodity hardware, at approximately $0, by our founding team.
With pre-registration, published negatives, and dated self-retractions. Not a physics record. An access-and-discipline result.
How to read these numbers
- Post-selected
- — runs that fail a detection check are discarded before scoring; the acceptance rate is always stated.
- Single-basis vs two-basis
- — protecting one error type is classical memory; a qubit needs both. We label which one every result is.
- Detection vs correction
- — detection flags errors and discards; correction fixes them mid-run. Ours detect.
- Encoded vs fault-tolerant
- — encoded means the state lives in a code; fault-tolerant is a far higher bar we do not claim.
- Per-run vs per-cycle
- — error rates only compare when the unit of exposure matches; we never mix them.
- Rented hardware
- — every measurement ran on IBM Heron-class cloud processors as a paying customer. We own no quantum hardware.
Three-basis logical Bell fidelity, [[4,2,2]] code
We prepared the logical Bell state of the [[4,2,2]] error-detecting code and measured all three logical correlators, each in its own circuit at 20,000 shots. Post-selecting into the codespace gives a logical-state infidelity near 6×10⁻⁴ — confidence interval tightened by a raw-array re-decode on 2026-08-15.
Caveat Distance-2 detection code, post-selected (~96% acceptance) — encoded and detected, not error correction. Rented IBM hardware. full note
Encoded logical qubits certified simultaneously
Thirty-one independent [[4,2,2]] logical Bell pairs held at once on a 156-qubit Heron processor — every block above the entanglement-witness separability bound, on calibration-ranked native couplers with zero added SWAPs.
Caveat 31 independent pairs — a fleet, not one 62-qubit state. Certified block-wise, not jointly: all 31 blocks passing in the same shot happens in 9.4% (Z) / 6.0% (X) of shots. Detection code, post-selected; witness-certified 31/31. Rented hardware. full note
Repetition-code ladder, distance 3 → 5
Failures fell from 22 to 4 per 100,000 shots when the code distance grew from 3 to 5, decoded with a detector-error-model matching decoder over the full detector history; a separate 20,000-shot run reproduced the direction (2 → 0 failures), too few events to re-measure the factor.
Caveat One-basis (bit-flip); one measured suppression step, not a below-threshold ladder. Rented hardware. full note
The connectivity wall, measured
Running the rotated surface code in both bases on degree-3 heavy-hex hardware, the distance-3 code showed a per-cycle logical error rate of 0.152 (Z basis), and by distance 5 the code was fully decohered — indistinguishable from chance in both bases — while the same code and decoder suppress errors (Λ ≈ 2.0) on an ideal degree-4 lattice in simulation. What we measured is what the missing degree costs.
Caveat A measured negative about lattice connectivity, not a ranking of anyone’s device. Figure re-decoded 2026-08-15; simulation and hardware never share an axis. full note
Hardware-aware layout: fewer gates, zero added SWAPs
Rebuilding a failed scattered layout into six local clusters cut the transpiled two-qubit gate count from 3,710 to 615 for the same circuit; separately, 630 logical two-qubit gates routed to exactly 630 — zero added SWAPs — on a 127-qubit induced path.
Caveat Compiler metrics, not device performance — our own before/after against the default toolchain. full note
Encoded exceeded unencoded on the same job
On a single job, the encoded logical Bell state scored higher than the bare physical Bell state on the Z-basis leg — 99.10% vs 98.54% — and modest, replicated detection gains appeared across repeated runs.
Caveat One-basis leg, post-selected detection at distance 2 — not correction. full note
A classical block code, exhaustively verified
A classical binary concatenated code — single brackets, not a quantum code — whose minimum distance of 12 was verified exactly by enumerating all 65,535 nonzero messages. The encoder/decoder ships with passing tests as packet error correction.
Caveat Classical code over GF(2) — not a quantum code. Distance verified by exhaustive enumeration. full note
For the record
Measurement notes, in full.
BELL Distance-2 detection code, post-selected (~96% acceptance); the textbook p→p² suppression, so we quote no improvement factor. The measured correlators coincide with the stabilizers of one native coupler pair, and the circuit is Clifford — classically simulable. Not error correction, no QEC cycles, not unconditional, no logical gate, no real-time loop. Honest label: encoded + detected. Encoded [[4,2,2]] Bell states are published prior work on several platforms, including this one; we claim no first. Raw per-shot arrays are archived and the number re-derives offline from them; no third party has verified this result — the circuit is depth 7 and costs nothing to re-run. ↩
FLEET A fleet of 31 independent pairs, not one 62-qubit entangled state. Distance-2 detection code, post-selected: mean acceptance 92.1%, joint acceptance across all 31 blocks 7.8% — post-selection does not scale, which is precisely why detection is not correction at scale. 31/31 blocks above the 0.5 bound with full confidence intervals clearing it (raw-array re-decode, 2026-08-15; mean witness 0.9964, min 0.9790). Rented hardware. ↩
LADDER One-basis (bit-flip): a repetition code protects a classical bit, not a qubit, and can never be a fault-tolerant qubit. One measured suppression step to a ~1×10⁻⁵ per-cycle floor: the d=5 and d=7 rates are statistically indistinguishable, so this is not a below-threshold ladder. Rounds = d, so state preparation and measurement are not separated from the per-round rate. Our software refuses to quote a suppression ratio with fewer than 5 events. Rented hardware. No quantum advantage is claimed. ↩
TAX A measured negative, published deliberately: a statement about lattice connectivity, not a ranking of anyone’s device. Published below-threshold demonstrations run on degree-4 lattices; we ran on degree-3. At distance 5 the decoded error rate is statistically indistinguishable from chance in both bases, so no suppression ratio is measurable on this lattice — an earlier per-ratio figure from these runs was retired on 2026-08-15 after a raw-array re-decode found a clamp artifact, and this page reports the re-decoded numbers. SWAP routing inflates the two-qubit gate count several-fold with distance; our transpilation was not connectivity-optimized. The simulation figure is simulation — it never sits on the same axis as the hardware number. Newer superconducting roadmaps are moving to higher-connectivity lattices; this measurement quantifies what the missing connectivity costs. This is the question our chip design starts from. ↩
LAYOUT Compiler and transpilation metrics on rented heavy-hex topology — gate-count and routing facts about circuit compilation, not device-performance or fidelity claims. Our own before/after against the default toolchain, not a competitor comparison. Calibration-ranked placement self-validates: the worst-calibration block was the lowest-witness block. ↩
CONTROL One-basis leg only; post-selected detection at distance 2 — not correction. The v1 X-basis run failed on a translation bug and is preserved, marked do-not-cite, rather than deleted. Detection gains: raw 0.563 → 0.705, reproduced 0.497 → 0.579. Points, not factors. ↩
CLASSICAL Classical, over GF(2): a [10,4,4] inner code crossed with a [7,4,3] Hamming outer code, rate 0.229. Honesty note: the Griesmer bound allows [35,16,12], so this construction is about twice as long as optimal — correct and tested, not record-setting. There is no quantum code of this name. ↩
Methods