Reducing the error rate of a superconducting logical qubit using analog readout information

Understand

Quantum error correction enables the preservation of logical qubits with a lower logical error rate than the physical error rate, with performance depending on the decoding method.

• Traditional error decoding approaches, relying on the binarization (`hardening') of readout data, often ignore valuable information embedded in the analog (`soft') readout signal.
• We present experimental results showcasing the advantages of incorporating soft information into the decoding process of a distance-three ($d=3$) bit-flip surface code with transmons.
• To this end, we use the $3\times3$ data-qubit array to encode each of the $16$ computational states that make up the logical state $\ket{0_{\mathrm{L}}}$, and protect them against bit-flip errors by performing repeated $Z$-basis stabilizer measurements.