Reducing the error rate of a superconducting logical qubit using analog readout information (2403.00706v2)

Abstract: 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. To infer the logical fidelity for the $\ket{0_{\mathrm{L}}}$ state, we average across the $16$ computational states and employ two decoding strategies: minimum weight perfect matching and a recurrent neural network. Our results show a reduction of up to $6.8\%$ in the extracted logical error rate with the use of soft information. Decoding with soft information is widely applicable, independent of the physical qubit platform, and could reduce the readout duration, further minimizing logical error rates.

• The paper demonstrates a 6.8% reduction in logical error rate by leveraging analog readout data in surface code error correction.
• It employs both MWPM and neural network decoders to adapt soft readout signals for improved qubit fidelity.
• The findings highlight potential for scalable quantum error correction on 17-qubit superconducting platforms and beyond.

Reducing the Error Rate of a Superconducting Logical Qubit Using Analog Readout Information

The paper "Reducing the error rate of a superconducting logical qubit using analog readout information" addresses a pertinent challenge in quantum error correction (QEC): the integration of soft information to enhance the fidelity of logical qubits. Specifically, this research investigates methods to optimize the error correction of a distance-three ($d=3$) bit-flip surface code by utilizing analog ('soft') readout data as opposed to conventional binary ('hard') readout processes. This approach is applied to a 17-qubit superconducting platform, prominently utilizing transmons.

The authors present empirical findings demonstrating a significant reduction in logical error rates by incorporating soft measurement data. A reduction of up to 6.8% in the logical error rate is achieved using a minimum-weight perfect matching (MWPM) decoder and a recurrent neural network (NN) decoder. The gain from soft decoding is uniform across the varied qubit platforms, suggesting a promising protocol applicable beyond the specific experimental setup.

Highlights and Methodology

In addressing quantum error correction, most efforts center around the development of sophisticated decoding algorithms. However, conventional strategies often rely on binarization of measurement data, ignoring potentially rich information contained within the analog signals. This paper builds on previous proposals advocating for soft information in decoding phases. Significant attention is given to adapting the MWPM and NN decoders to leverage continuous readout signals, thereby enabling more informed decision-making processes during error correction.

The experiment employs a superconducting device consisting of a 9x9 array of data qubits arranged into a $d=3$ surface code. The system continuously performs $Z$-basis stabilizer measurements which are subsequently corrected using the aforementioned decoders. The dos instructions extend to using calibration data to fit probability density functions (PDFs) for readout classification, ensuring that the decoding process correctly factors in measurement uncertainties.

Numerical Results and Implications

Two decoding strategies—MWPM and NN—have been employed. Both strategies initially rely on constructing a decoding graph through pairwise correlation methods. The MWPM approach benefits from dynamic edge weighting adjustments based on per-shot soft information, which is a departure from average-based weight assignments. In contrast, the NN decoder is trained directly on experimental data, bypassing the need for pre-defined noise models. This flexibility allows the NN to inherently learn from variable fidelities and adapt accordingly.

The use of soft information shows demonstrable improvements in logical qubit performance. For the MWPM decoder, the logical error rate decreases significantly, while the NN approach achieves even higher accuracy, illustrating potential for more extensive usage of neural networks in QEC environments moving forward.

Future Directions

The results of this research emphasize the potential for soft information to reduce error rates in scalable quantum devices. Future studies could explore further reduction in readout duration that this approach allows, potentially minimizing errors even before data is fed into a decoder. Additionally, the integration of more sophisticated neural network architectures, trained on diverse datasets, may enhance accuracy and robustness of error correction in increasingly larger quantum systems. The efficiencies gained in this paper necessitate advancing beyond $d=3$ surface codes, trialing these methods on higher-distance codes where gains may become more pronounced.

Overall, the advances demonstrated in this work underscore a critical evolutionary step in quantum error correction methodologies, combining experimental empiricism with evolving computational strategies for real-world quantum computation improvements.