Suppressing quantum errors by scaling a surface code logical qubit

Abstract: Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance scaling across multiple code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, both in terms of logical error probability over 25 cycles and logical error per cycle ($2.914\%\pm 0.016\%$ compared to $3.028\%\pm 0.023\%$). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a $1.7\times10^{-6}$ logical error per round floor set by a single high-energy event ($1.6\times10^{-7}$ when excluding this event). We are able to accurately model our experiment, and from this model we can extract error budgets that highlight the biggest challenges for future systems. These results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.

• The paper shows that scaling up the surface code with a 72-qubit, distance-5 configuration significantly lowers logical error probabilities compared to smaller distance-3 codes.
• The study employs rigorous experimental methods and simulations using Pauli and Pauli+ error models to accurately identify and mitigate error sources.
• The research underscores the importance of managing qubit coherence loss and leakage, paving the way for fault-tolerant quantum computing.

Suppressing Quantum Errors by Scaling a Surface Code Logical Qubit

The study, "Suppressing quantum errors by scaling a surface code logical qubit" conducted by Google Quantum AI examines the performance scaling of logical qubits with increasing code sizes within the framework of surface codes, utilizing superconducting qubits. This research aligns with the broader pursuit of developing practical quantum computing systems, which necessitates error rates exponentially lower than those achievable with current physical qubits. The team's findings contribute to this objective by demonstrating an instance where logical qubit performance is enhanced by increasing the number of physical qubits in the setup.

In this investigation, the team constructed a 72-qubit superconducting device integrating a distance-5 surface code, characterized by 25 data qubits and 24 measure qubits. This configuration was optimized to achieve more reliable logical qubit performance compared to an ensemble of 17-qubit distance-3 logical qubits. The measured error probabilities per cycle for both configurations were statistically analyzed, showing the larger distance-5 code had lower average logical error probability over 25 cycles, a crucial indicator of improved performance resulting from a larger code size.

A significant aspect of the study was the implementation of a distance-25 repetition code, measuring an exceptionally low logical error per round, facilitated by a single high-energy event detected during experimentation. By excluding this event, the error rate stood at $1.6 \times 10^{-7}$ underlining the potential for low-error quantum computation with judicious design and error management strategies.

The paper notes that error sources, such as coherence loss and qubit state leakage to non-computational levels, are persistent challenges affecting surface code performance. The team validated their experimental observations against simulations, utilizing a combination of Pauli and Pauli+ error models. This approach was critical for identifying dominant error contributors and understanding how logical qubit performance depends on component-level improvements.

The research underscores the importance of improvement at the component level— such as enhanced controlled-Z (CZ) gate performance and reduced crosstalk—highlighting the surface code's sensitivity to such parameters. A notable emphasis was placed on the impact of crosstalk and leakage as primary contributors to logical faults.

This work signifies an important milestone for scalable quantum error correction efforts. By achieving enhanced logical qubit performance, the paper details a novel demonstration of favorable error scaling with increased qubit numbers—a requirement for fault-tolerant quantum computing. The projection is to surpass error thresholds through continued refinement, aiming for quantum computing systems with logical error rates that facilitate practical quantum computational tasks.

In conclusion, the study effectively furthers the understanding of quantum error suppression through leveraging increased code distances, offering insights into error management at multiple levels within scaled systems. This integrates both empirical results and comprehensive modeling, illuminating pathways for the development of robust quantum computing architectures capable of efficiently addressing the demands of future quantum algorithms.