Verification and Postselection
Checking a freshly prepared encoded state and discarding it when a check fires trades extra attempts for higher-quality inputs to a computation.
Trading attempts for quality
Postselection means running a subroutine, testing its output, and keeping the result only when the test passes. In fault tolerance this appears mainly in state preparation and magic-state distillation. A verification circuit measures whether a dangerous error is present; if it is, the state is thrown away and the routine restarts. The kept states are cleaner than the raw ones.
Where it is used and where it is not
Postselection is acceptable at preparation time because discarding a fresh ancilla costs only time, not encoded data. It cannot be used on the main computational qubits during an algorithm, because throwing away a logical qubit mid-computation would destroy the running state. The art is confining postselection to offline, restartable stages.
- Verification detects encoding or distillation faults before use.
- Failed checks trigger a discard-and-retry, never a mid-computation abort.
- Acceptance probability sets the average number of attempts.
- Heralded errors are far cheaper to handle than silent ones.
The efficiency of a postselected routine is governed by its acceptance rate. If most attempts pass, overhead is small; if the check rejects too often, the routine stalls. Distillation circuits are engineered so that clean inputs pass almost always and only genuinely faulty runs are rejected.
Heralding, the general idea of turning a silent error into a flagged, detectable event, connects postselection to flag qubits and to erasure-style noise. A machine that can convert many of its errors into heralded losses gains a large advantage, because heralded errors are located for free and are far easier to correct than unknown Pauli errors.