Glossary

One qubit's worth of protected information, stored across many physical qubits so that errors can be detected and undone.

Easy to get wrong: The count of logical qubits is not the size of the machine. A single logical qubit at code distance 11 occupies 242 physical qubits, and routing space and magic-state factories are on top of that.

Seen in use on /workbench

The most studied way to build a logical qubit, laying physical qubits on a two-dimensional grid where only neighbours interact.

Easy to get wrong: It only suppresses errors below its threshold. Above that, adding more qubits makes the logical error rate worse, not better.

Seen in use on /qec

The smallest number of physical errors that can corrupt the encoded information without being noticed.

Easy to get wrong: Distance d corrects only (d−1)/2 errors, not d. A distance-3 code corrects one error and *miscorrects* two — the correction itself introduces the failure.

Seen in use on /qec/syndromes

A measurement a code makes repeatedly that returns the same answer as long as nothing has gone wrong.

Easy to get wrong: Stabilizers never measure the stored data — doing so would destroy the superposition. They only report whether they were disturbed.

Seen in use on /qec/syndromes

The pattern of which stabilizers were disturbed: the only information a decoder gets about an error.

Easy to get wrong: An all-zero syndrome does not mean nothing happened. An error heavy enough to commute with every stabilizer is applied silently, which is exactly what a code's distance limits.

Seen in use on /qec/syndromes

The algorithm that reads a syndrome and decides what correction to apply.

Easy to get wrong: A decoder succeeds when its guess differs from the real error by a stabilizer, not when it guesses correctly. Scoring by exact match reports failures on codes that in fact corrected everything.

Seen in use on /decoders

A decoder that pairs up detection events so the total 'distance' between paired events is as small as possible.

Easy to get wrong: Fast and accurate on surface codes, but its accuracy depends on the noise matching the model it was given. A decoder tuned for depolarizing noise can do poorly when readout error dominates.

Seen in use on /qec/lab

The physical error rate below which adding more qubits to a code helps, and above which it hurts. Roughly 1% for the surface code.

Easy to get wrong: Results measured above threshold say nothing about behaviour below it. The two are different regimes, not two points on one curve.

Seen in use on /qec/lab

How often the protected information is corrupted despite error correction, per round or per computation.

Easy to get wrong: Zero observed failures is not a rate of zero. Zero failures in 10,000 shots bounds the rate below roughly 3.8×10⁻⁴ and says nothing about whether it is 10⁻⁵ or 3×10⁻⁴.

Seen in use on /leaderboard

How often an individual hardware operation goes wrong.

Easy to get wrong: It is an assumption in a simulation, not a measurement of your hardware, unless the record says otherwise.

Seen in use on /qec/lab

The description of how a device is assumed to fail, used to simulate it.

Easy to get wrong: Two decoders compared under different noise models are not being compared. Depolarizing, readout and leakage noise stress a decoder in different ways.

Seen in use on /qec/lab

The simplest useful noise model: with some probability, a random Pauli error replaces the intended state.

Easy to get wrong: It is the friendliest realistic model. A decoder that only works under depolarizing noise has not been shown to work.

A qubit escaping the two states it is supposed to occupy, into a third level the code cannot describe.

Easy to get wrong: Standard decoders assume it cannot happen, so leakage errors are not merely undetected but outside the model entirely.

The quantum equivalent of a bit, which can be in a combination of 0 and 1 rather than only one of them.

Easy to get wrong: A qubit is not "both 0 and 1 at once" in any useful sense. It has an amplitude for each, and only the relative sizes and phases of those amplitudes affect anything you can measure.

Seen in use on /workbench

The text format for writing quantum circuits that most tools can read.

Easy to get wrong: Versions 2 and 3 are different languages. Several frameworks read only version 2, so exporting to them silently loses anything version 3 added — single-bit conditions among them.

Seen in use on /workbench

How many layers of operations run one after another, rather than side by side.

Easy to get wrong: Depth, not gate count, sets how long a circuit takes and how much time it has to decohere. A wide shallow circuit and a narrow deep one with the same gate count behave completely differently.

Seen in use on /workbench

An operation acting on two qubits at once, which is how entanglement is created.

Easy to get wrong: These are the expensive, error-prone operations on real hardware — typically ten times worse than single-qubit gates, so the two-qubit count matters more than the total.

Rewriting a circuit so it only uses gates the device has, on qubits that are physically connected.

Easy to get wrong: It is not free. Connecting distant qubits inserts SWAP gates, and the transpiled circuit can be several times deeper than what you wrote.

Seen in use on /workbench

The family of gates that are easy to simulate classically — H, S, CNOT and their combinations.

Easy to get wrong: A circuit made only of Clifford gates needs no magic states and offers no quantum advantage. The T gates are what make a circuit both useful and expensive.

The three basic single-qubit errors and operations: X, Y and Z.

Easy to get wrong: Y is not a separate kind of error — it is X and Z together, which is why a code that catches both catches Y automatically.

Seen in use on /qec/syndromes

The complete description of a quantum state, as one amplitude per possible outcome.

Easy to get wrong: It doubles in size with every qubit, so a statevector simulation is exact and small only. It also does not survive measurement — measuring collapses the state.

Seen in use on /workbench

How many T gates a circuit needs. The standard measure of a fault-tolerant circuit's cost.

Easy to get wrong: Each T gate consumes a magic state that must be manufactured, and the factories doing that are usually the majority of the machine — often more than 90% of its physical qubits.

Seen in use on /workbench

A three-qubit controlled-controlled-NOT gate, common in arithmetic.

Easy to get wrong: Usually costed as 4 T gates, so a circuit's Toffoli count is a large part of its real expense even though it looks like one operation.

A specially prepared state that lets a fault-tolerant computer perform a T gate, which it cannot do directly.

Easy to get wrong: They cannot be prepared reliably, only distilled from many noisy copies — which is why they dominate the cost.

Seen in use on /workbench

Consuming many low-quality magic states to produce fewer better ones.

Easy to get wrong: It only improves a state below a fixed point. Above roughly 1/√35 for the standard protocol, each round makes things worse and no number of rounds helps.

The total probability of failure you are willing to accept across a whole computation.

Easy to get wrong: It is divided among every logical qubit and every cycle, so a modest-sounding budget implies a very small per-operation error rate.

Seen in use on /workbench

Performing operations between logical qubits by merging and splitting their patches on the grid.

Easy to get wrong: It needs free space beside the data to move information through, so a register of n logical qubits occupies more than n patches — Microsoft's estimator uses 2n + ⌈√(8n)⌉ + 1.

How many times a circuit is run to build up statistics from its measurements.

Easy to get wrong: Every quantity estimated from shots carries roughly 1/√N of noise. Doubling precision costs four times the shots.

Seen in use on /workbench

How much an estimate would wobble if you repeated the whole experiment.

Easy to get wrong: A number without one is not a measurement. Two results whose error bars overlap have not been shown to differ.

Seen in use on /leaderboard

Post-processing noisy results to estimate what a noiseless machine would have produced.

Easy to get wrong: It buys accuracy with variance and shots, never for free. Zero-noise extrapolation can make a result worse when the extra uncertainty exceeds the bias it removed.

Seen in use on /workbench

The average of a measurement over many shots, rather than any single outcome.

Easy to get wrong: Two very different states can share an expectation value. A Bell pair and two independent coin flips give identical single-qubit averages and differ only in their correlations.

Seen in use on /workbench

Whether a result came from a simulator, real hardware, or synthetic demo data.

Easy to get wrong: A simulated result is never evidence about hardware. This registry refuses results labelled HARDWARE because it cannot verify them.

Seen in use on /runs

A fingerprint of everything that defines a result, so an identical rerun is recognisable.

Easy to get wrong: A matching hash proves the record is self-consistent, not that the numbers came from where it claims. Anyone can compute a correct hash over a fabricated result.

Seen in use on /runs

A versioned definition of an experiment, so two people can run the same thing.

Easy to get wrong: Runs from different suite versions are not comparable, and a leaderboard that mixes them is a ranking of different experiments.

Seen in use on /benchmarks

A range that would contain the true value most of the time, given the data.

Easy to get wrong: It is not a range the true value is 95% likely to sit in for this one experiment — it is a statement about the procedure, repeated.

Seen in use on /leaderboard