A framework of partial error correction for intermediate-scale quantum computers
arXiv:2306.15531 · doi:10.1038/s41534-026-01301-3
The paper proposes a framework for using error correction on only a subset of qubits in intermediate‑scale quantum computers, showing that mixing error‑corrected and noisy qubits can slow down decoherence and improve circuit performance under Pauli and depolarizing noise.
Abstract
As quantum computing hardware steadily increases in qubit count and quality, one important question is how to allocate these resources to mitigate the effects of hardware noise. In a transitional era between noisy small-scale and fully fault-tolerant systems, we envisage a scenario in which we are only able to error-correct a fraction of the qubits required to perform an interesting computation. In this work, we develop concrete constructions of logical operations on a joint system of a collection of noisy and a collection of error-corrected logical qubits. Within this setting and under Pauli noise assumptions, we provide analytic evidence that brick-layered circuits display on average slower concentration to the ``useless'' uniform distribution with increasing circuit depth compared to fully noisy circuits. We corroborate these findings by numerical demonstration of slower decoherence with an increasing fraction of error-corrected qubits under depolarizing noise acting at the circuit level. We find that this advantage only manifests when the number of error-corrected qubits passes a specified threshold which depends on the number of couplings between error-corrected and noisy registers.
19+20 pages, 8+11 figures, comments welcome