Leakage and Seepage
Leakage is population escaping the computational subspace into higher levels; seepage is its return, and both break the assumptions of standard error correction.
The Two Directions
A qubit is defined by two levels, but the physical systems that host qubits have more. A transmon is a multi-level anharmonic oscillator; leaving the ground and first-excited states available for computation leaves the second-excited state and beyond as unwanted destinations. Leakage is the process by which population moves out of the computational space into these higher levels. Seepage is the reverse, population returning from a higher level back into the computational space, often into an unpredictable state.
Why Leakage Is Especially Harmful
Ordinary errors keep the qubit inside its two-level space and can be described as bit flips and phase flips, which error-correcting codes are designed to handle. Leakage violates this: a leaked qubit is neither zero nor one but somewhere else entirely. Standard syndrome extraction can misinterpret it, and a leaked qubit can spread errors to its neighbors through the gates and couplings meant only to act within the computational space. Because leaked population may persist for many cycles, it causes correlated errors in time as well.
- Leakage: computational to non-computational, often during fast gates.
- Seepage: non-computational back to computational, usually into a mixed state.
- Error correction assumes a two-level system, which leakage violates.
Sources
Leakage arises mainly from fast, strong control pulses whose spectrum overlaps a nearby transition, from two-qubit gates that deliberately use a higher level and fail to return all population, and from thermal excitation. Single-qubit leakage is suppressed by DRAG pulse shaping; two-qubit gate leakage is minimized by careful pulse trajectories and calibration.
Managing Leakage in Error Correction
Because leakage cannot be removed by the code alone, dedicated leakage-reduction operations are inserted. These reset schemes deliberately return any leaked population to the computational space, converting a leakage event into an ordinary error the code can then handle. Interleaving such operations with syndrome cycles keeps leakage from accumulating and is a required part of practical fault-tolerant operation.