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 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

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

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 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.

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.

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