Repeated quantum error correction on a continuously encoded qubit by real-time feedback (1508.01388v2)

Abstract: Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be compatible with universal fault-tolerant computations, it is essential that the states remain encoded at all times and that errors are actively corrected. Here we demonstrate such active error correction on a continuously protected qubit using a diamond quantum processor. We encode a logical qubit in three long-lived nuclear spins, repeatedly detect phase errors by non-destructive measurements using an ancilla electron spin, and apply corrections on the encoded state by real-time feedback. The actively error-corrected qubit is robust against errors and multiple rounds of error correction prevent errors from accumulating. Moreover, by correcting correlated phase errors naturally induced by the environment, we demonstrate that encoded quantum superposition states are preserved beyond the dephasing time of the best physical qubit used in the encoding. These results establish a powerful platform for the fundamental investigation of error correction under different types of noise and mark an important step towards fault-tolerant quantum information processing.

• The paper demonstrates that repeated real-time feedback significantly extends the coherence of a continuously encoded qubit through active error correction.
• The methodology employs non-destructive stabilizer measurements using an ancilla electron spin to ensure high-fidelity error syndrome detection on nuclear spins.
• Results show that the implemented three-qubit code effectively corrects single phase errors, marking a key milestone toward fault-tolerant quantum computation.

Repeated Quantum Error Correction on a Continuously Encoded Qubit by Real-Time Feedback

The paper under discussion presents a comprehensive paper on quantum error correction (QEC) applied to a continuously encoded qubit using real-time feedback on a diamond quantum processor. The researchers demonstrate the efficacy of active error correction, which is an essential characteristic for universal fault-tolerant quantum computations. This work is crucial as it addresses one of the primary challenges in quantum information processing: maintaining the coherence of quantum states against errors induced by environmental and operational factors.

The authors encode a logical qubit in three long-lived nuclear spins and employ an electron spin as an ancilla to detect phase errors through non-destructive stabilizer measurements. This approach leverages a diamond-based quantum processor, where the logical qubit remains continuously protected and is subjected to multiple rounds of error correction to prevent error accumulation. By correcting correlated phase errors naturally induced by the environment, the paper showcases that encoded quantum superposition states can survive beyond the dephasing time of the individual physical qubits.

A notable aspect of this work is the implementation of stabilizer measurements using an ancilla electron spin. The measurements are performed in a non-destructive manner, which is pivotal to preserving the coherence of the logical qubit while performing frequent error detections. Post-measurement, the classical logic processes the outcomes to determine the error syndromes, allowing real-time feedback for active error correction. This methodology ensures that error corrections are applied before the coherence time expires, addressing a key experimental limitation in current quantum technologies.

The results indicate that the employed three-qubit code effectively corrects a single phase error on any individual qubit, as evidenced by the high fidelity of the logical qubit states post-correction. The process fidelity, when plotted against error probability, shows a characteristic non-linear dependency, affirming the robustness of the quantum error correction scheme against single-qubit errors.

On the theoretical front, this research validates the significance of stabilizer measurements as a part of continuous QEC protocols. Moreover, the ability to improve the dephasing time through error correction, surpassing the best-performing individual qubit, marks a significant advancement toward fault-tolerant quantum computation. The experimental setup and methodology set a solid foundation for exploring broader applications, including networked quantum computing and entanglement purification.

The findings underscore the pivotal role of non-destructive ancilla readouts and feedback mechanisms in achieving systems that can perform universal computations on logical qubits robustly. Future work could focus on enhancing the fidelity of these processes, potentially through advancements such as optimal control techniques and better defect engineering in quantum materials. Additionally, the integration of these results with recent developments in entangling distant quantum nodes can pave the way for realizing robust quantum networks.

In conclusion, this research provides significant progress in understanding and implementing active quantum error correction in a real-world quantum processor. The results and methodologies documented here are vital for the ongoing development of scalable quantum information systems that can operate efficiently under various noise conditions.