Hardware & Errors
Leakage Error
An error in which a qubit leaves its two intended states and ends up in another energy level or is lost altogether.
Definition
A qubit is supposed to live in two states, 0 and 1. But the physical object that carries it, such as a superconducting circuit or an atom, has more energy levels, and a gate or noise can push the qubit into one of them. That is leakage. Leakage is especially harmful because ordinary error-correcting codes are built to fix bit and phase flips, and a qubit sitting in a third state can spread errors to its neighbors for many rounds before it is noticed.
In depth
In transmons, the qubit is the lowest two levels of an anharmonic oscillator, and fast gates can excite the third level because it is only a few hundred megahertz away. Techniques such as DRAG pulses add a quadrature component to the drive that cancels transitions to the third level, and they cut leakage per gate to the order of 0.01 percent or below. But small leakage accumulates, and in error-correction experiments leaked qubits can persist for many cycles, corrupting syndrome measurements.
Error-correction groups therefore add leakage reduction units, circuits that return a leaked qubit to the computational space, and decoders that account for leakage. Google's experiments with the surface code showed that leakage is a significant source of correlated errors, and reducing it was part of reaching below-threshold performance on Willow. Researchers also study dual-rail encoding, where a qubit is a single excitation in one of two resonators, which turns leakage into an observable erasure.
In neutral atom and trapped ion machines, the analogous error is atom or ion loss, where the carrier leaves the trap. This can be detected by imaging, which makes it an erasure error whose location is known, and erasure errors are easier to correct than unknown errors, since the code needs less redundancy. Convert-to-erasure designs, proposed by Wu and coauthors and by Kubica and coauthors for atoms and demonstrated in several labs, exploit this property deliberately.
Technical Definition
Leakage is a transition out of the computational subspace spanned by the qubit states into other levels, such as the second excited state of a transmon, or the loss of an atom or ion from its trap. Leaked states are outside the Hilbert space assumed by the circuit and by standard error-correction decoders. Mitigation includes leakage reduction units, pulse shaping, and conversion of leakage into erasure errors that can be detected and located.
Visual Explanation: An Analogy
Imagine a light switch that can only be on or off, but sometimes it jams halfway in a position that neither state describes. Anything wired to it behaves oddly until someone notices and resets it.
Key facts
| Item | Detail |
|---|---|
| Cause | Population in non-computational levels after gates or noise, or physical loss of the qubit carrier |
| Typical rates | Order 10^-4 to 10^-3 per gate, depending on the platform and pulse design |
| Mitigation | DRAG pulses, leakage reduction units, and fast reset |
| Erasure conversion | Making leakage or loss detectable, which improves code thresholds |
| Where it matters most | Quantum error correction, where leaked qubits cause correlated errors |
Where the idea comes from
Leakage was recognized as a problem for early superconducting qubits, and the DRAG pulse technique of Motzoi and coauthors in 2009 reduced it. With surface code demonstrations in 2021 and 2023, leakage reduction became standard, and the idea of erasure conversion in 2022 and 2023 gave it a positive spin.
Real-World Use Cases
- Calibrating gates to minimize population outside the qubit space.
- Adding leakage reduction units to error-correction circuits.
- Designing erasure-converted qubits for atoms and superconducting dual-rail encodings.
- Modeling realistic noise in decoders and simulations.
How it differs from related ideas
- A bit flip keeps the qubit in the computational space, while leakage takes it out.
- An erasure error is a known-location error and easier to correct than a random error.
- Leakage is different from decoherence, which is loss of coherence within the qubit space.
Common Misconceptions
- Leakage is not rare enough to ignore in error-correction experiments. It affects logical error rates.
- You cannot simply measure leakage away. Standard readout often cannot distinguish a leaked state from the 1 state.
- Leakage is not unique to superconducting qubits. It appears as atom and ion loss in other platforms.
Frequently asked questions
What is a leakage error?
An error in which a qubit ends up in a state outside the two intended levels, or is physically lost.
Why is leakage dangerous for error correction?
A leaked qubit can persist and cause correlated errors in neighbors, which codes are poorly equipped to handle.
How can leakage help?
If it is detected and its location known, it becomes an erasure error, which is easier to correct.
Related Terms
Keep exploring
- Algorithm: Quantum Error-Correcting Codes (Shor Code, Surface Code)
- Hardware: Google Willow
- Hardware: Pasqal Fresnel (Orion generation)