Logical Qubit Milestones
A logical-qubit milestone is evidence that encoding improves a specified information-processing task under a stated comparison. The research problem is to connect demonstrations of state preparation, memory and individual gates to a reproducible progression toward useful computation. A count of encoded qubits cannot establish that progression by itself.
Required background. Logical benchmarking defines task-matched physical references and logical observables.
Logical protection has several thresholds
Section titled “Logical protection has several thresholds”Encoding demonstrates a map into a code space. Error detection demonstrates information about faults. Break-even demonstrates an advantage over a specified unencoded task. Suppression with increasing distance tests scalability in a measured regime. A universal protected gate set and a sustained algorithm are further claims, each needing its own evidence.
For independent logical flips with probability each round, a logical Pauli expectation behaves as
The fitted amplitude absorbs preparation and readout only when the model is appropriate. Drifting noise, leakage and correlated bursts can violate exponential decay. A lower fitted then need not mean a smaller total task failure probability.
Selected evidence and its boundary
Section titled “Selected evidence and its boundary”Established experimental result: the 2023 Google surface-code experiment compared distance-three and distance-five memories. The 2025 report extended below-threshold memory evidence and separately integrated a real-time decoder. These papers provide concrete distance comparisons, not permission to extrapolate indefinitely. Inspect the primary reports and their supplements for which bases, durations and decoding procedures were measured. 2023 report, 2025 report.
Active question: whether suppression survives universal operations, longer missions, changing calibrations and rare correlated faults. Conditional fidelity after postselection is a legitimate metric when accompanied by acceptance, but it addresses a different task from deterministic computation. Report and together.
A fair ledger records date, code, physical resources, rounds, logical operation, measured observable, physical baseline, decoder information, acceptance and uncertainty. Label simulated projections separately from measurements. Do not average several unrelated logical operations into a single milestone score.
Open problems worth isolating
Section titled “Open problems worth isolating”Can one detect an error floor before it contaminates an application-scale extrapolation? Can logical gate benchmarks expose correlations between qubits in the same code block? Which randomized or adversarial workloads reveal failure modes hidden by memory experiments? These questions connect to verification and hardware scaling.
Graduate project: stress-test a suppression claim
Section titled “Graduate project: stress-test a suppression claim”Using public numerical data from a distance-scaling paper, fit both an exponential-in-distance model and a model with a nonzero floor. Publish the extracted data, fit code, uncertainty intervals and predictive comparison on withheld distances or durations. A laptop and standard statistical libraries are sufficient; do not infer raw shot counts from a plotted error bar without justification.
The baseline is the reported model. Failure tests include excluding a single calibration period, separating measurement bases, and fitting accepted and unconditional outcomes when both exist. If the data cannot distinguish a floor, the deliverable is an upper bound on the extrapolation supported by those data. Progress to research by designing the additional duration or distance measurements that maximally separate the models, then collaborating on their acquisition.
Entry points and review scope
Section titled “Entry points and review scope”Read both reports as measurement contracts before comparing their headline values. Sources were checked on 11 October 2026; the selected milestone evidence is from 2023 and 2025, not an exhaustive October 2026 leaderboard.