Encoding a magic state with beyond break-even fidelity (2305.13581v2)

Abstract: To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from noise~\cite{Harper2019,Ryan-Anderson2021,Egan2021fault, Chen2022calibrated, Sundaresan2022matching, ryananderson2022implementing, Postler2022demonstration, GoogleAI2023}. We can complete a universal set of logic gates by producing special resources called magic states~\cite{Bravyi2005universal,Maier2013magic, Chamberland2022building}. It is therefore important to produce high-fidelity magic states to conduct algorithms while introducing a minimal amount of noise to the computation. Here, we propose and implement a scheme to prepare a magic state on a superconducting qubit array using error correction. We find that our scheme produces better magic states than those we can prepare using the individual qubits of the device. This demonstrates a fundamental principle of fault-tolerant quantum computing~\cite{Shor96}, namely, that we can use error correction to improve the quality of logic gates with noisy qubits. Additionally, we show we can increase the yield of magic states using adaptive circuits, where circuit elements are changed depending on the outcome of mid-circuit measurements. This demonstrates an essential capability we will need for many error-correction subroutines. Our prototype will be invaluable in the future as it can reduce the number of physical qubits needed to produce high-fidelity magic states in large-scale quantum-computing architectures.

• The paper presents an error-corrected magic state preparation protocol that reduces infidelity from O(ε) to O(ε²) using a four-qubit error-detecting code.
• The protocol employs adaptive circuit elements triggered by mid-circuit measurements to dynamically adjust operations and enhance state fidelity.
• Experimental results confirm that the method outperforms traditional techniques and unencoded approaches, paving the way for scalable quantum computation.

Encoding a Magic State with Beyond Break-Even Fidelity

The paper at hand, "Encoding a magic state with beyond break-even fidelity," presents a scheme for preparing high-fidelity magic states on superconducting qubit arrays. Preparing these states is crucial for executing large-scale quantum algorithms effectively, as magic states serve as vital resources for implementing non-Clifford gates. The work proposes using a four-qubit error-detecting code on a heavy-hexagonal lattice of superconducting qubits, demonstrating an improvement over baseline methods that rely on individual noisy qubits.

Main Contributions

1. Error-Corrected Magic State Preparation: The authors present a protocol for encoding a magic state through an innovative error-suppressed circuit. This preparation leverages a four-qubit code known for its ability to detect and mitigate errors, suppressing the infidelity of the encoded state as $O(\epsilon^2)$ compared to the $O(\epsilon)$ infidelity typically seen in standard encoding methods.
2. Adaptive Circuit Implementation: The paper introduces adaptive circuit elements that adjust based on mid-circuit measurement outcomes, further refining the magic state yield. This represents a significant step in evolving error correction practices, which must account dynamically for errors detected mid-operation and conditionally adjust subsequent operations to correct them.
3. Experimental Results: The team demonstrates that their magic-state preparation outperforms both traditional techniques and an idealized approach that directly manipulates two physical qubits. Notably, they achieved higher fidelity than the best-performing unencoded states of their device, indicating that substantial improvements can be realized even with current error rates.
4. Fault-Tolerant Logical Tomography: To verify the performance of the prepared magic states, the authors employ a "logical tomography" approach, which measures the logical rather than physical qubits directly. This method inherently possesses a robustness due to its error tolerance, and thus provides more reliable insights into the assessed state fidelity.

Implications and Future Prospects

The demonstrated improvement in magic state fidelity furthers the feasibility of practical quantum computations. By illustrating a protocol where error suppression effectively enhances the fidelity of qubits, this research directly impacts the scalability of quantum computers. The integration of real-time adaptive circuits marks progress towards fault-tolerant quantum computation—a necessary capability in large-scale quantum systems for tasks such as magic-state distillation and teleportation.

From a theoretical perspective, the methods and results discussed illuminate pathways for further refinement of pieceable fault tolerance. This paper indicates new possibilities for effectively combining error correction with error mitigation techniques, potentially setting a precedent for more extensive use of non-Clifford operations in fault-tolerant contexts.

Conclusion

"Encoding a Magic State with Beyond Break-Even Fidelity" provides substantial evidence that quantum error correction schemes can indeed improve the preparation fidelity of magic states on noisy qubits. As the community progresses toward error-tolerant, large-scale quantum machines, methods like those proposed herein will be foundational to achieving the necessary reliability and efficiency. This work sets the stage for continued developments in error management and adaptive real-time quantum processing, pivotal for unlocking the full potential of quantum computation.