Short answer: Leakage is when a qubit leaves its two computational states and ends up in a higher energy level. It is a serious problem for quantum error correction because it persists, spreads to neighbouring qubits and creates correlated errors that standard codes are not built to handle. Leakage reduction units (LRUs) are operations that return leaked population to the computational states. Papers from 2021 to 2023 propose and demonstrate them on superconducting qubits, with results on small error-correction experiments.
Why leakage is different
A 2023 paper in Nature Physics says leakage out of the two computational states into other energy states represents a major challenge for quantum error correction. During an error-corrected algorithm, leakage builds over time and spreads through multi-qubit interactions, leading to correlated errors that degrade the exponential suppression of logical error with scale. The paper says a key assumption of error correction is that physical errors are sufficiently uncorrelated in space and time, while a leaked qubit can induce errors on several neighbours and even make them leak too. A 2021 PRX Quantum paper adds that quantum error correction codes do not provide inherent protection against leakage, which is present in leading platforms such as superconducting qubits.
A hardware-efficient proposal
The 2021 PRX Quantum paper proposes a scheme with two LRUs for a transmon-based surface code, which it says needs no extra hardware or QEC-cycle time compared with previous proposals. For data qubits, a microwave drive transfers leakage to the readout resonator, where it decays quickly. For ancilla qubits, a pi pulse between the first and second excited states is applied conditioned on the measurement outcome. In density-matrix simulations of a distance-3 surface code, the authors show the average leakage lifetime falls to almost one QEC cycle even when the LRUs have limited fidelity, with a significant reduction in logical error rate. They say this opens the prospect for near-term scalable demonstrations. This is a simulation result.
Experiments
A 2023 Physical Review Letters paper realizes and extends an all-microwave LRU for transmons proposed in earlier work. The authors report that it reduces leakage in the second and third excited transmon states with up to 99% efficacy in 220 nanoseconds, with minimal impact on the qubit subspace. As a first application, they show multiple simultaneous LRUs reducing the error detection rate and suppressing leakage buildup to within 1% in data and ancilla qubits over 50 cycles of a weight-2 stabilizer measurement.
The 2023 Nature Physics paper demonstrates a distance-3 surface code and a distance-21 bit-flip code on a quantum processor in which leakage is removed from all qubits in each cycle. The authors report a tenfold reduction in the steady-state leakage population of the data qubits and an average leakage population below 1 times 10 to the minus 3 across the device. They say the removal process returns the system efficiently to the computational basis, and that with this demonstration leakage can be contained, which they describe as resolving a key challenge for practical error correction at scale. That final judgment is the authors' own.
What this does not tell you
These experiments involve small codes on specific devices. They do not show leakage handled in a large fault-tolerant machine, and the figures depend on the hardware and cycle design.
FAQ
What is leakage?
A qubit leaving the two computational states for a higher energy level.
Why does it matter for error correction?
It spreads and causes correlated errors, which codes do not protect against by themselves.
What is a leakage reduction unit?
An operation that returns leaked population to the computational states.
How effective was it?
One paper reports up to 99% efficacy in 220 ns, another a tenfold lower steady-state leakage population.
Is the problem solved?
The authors of one paper say leakage can be contained, but the experiments are small.
All field notes