Analog information decoding of bosonic quantum LDPC codes (2311.01328v2)

Abstract: Quantum error correction is crucial for scalable quantum information processing applications. Traditional discrete-variable quantum codes that use multiple two-level systems to encode logical information can be hardware-intensive. An alternative approach is provided by bosonic codes, which use the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information. Two promising features of bosonic codes are that syndrome measurements are natively analog and that they can be concatenated with discrete-variable codes. In this work, we propose novel decoding methods that explicitly exploit the analog syndrome information obtained from the bosonic qubit readout in a concatenated architecture. Our methods are versatile and can be generally applied to any bosonic code concatenated with a quantum low-density parity-check (QLDPC) code. Furthermore, we introduce the concept of quasi-single-shot protocols as a novel approach that significantly reduces the number of repeated syndrome measurements required when decoding under phenomenological noise. To realize the protocol, we present a first implementation of time-domain decoding with the overlapping window method for general QLDPC codes, and a novel analog single-shot decoding method. Our results lay the foundation for general decoding algorithms using analog information and demonstrate promising results in the direction of fault-tolerant quantum computation with concatenated bosonic-QLDPC codes.

• The paper presents quasi-single-shot decoding protocols that leverage continuous syndrome data to minimize repeated measurements.
• It proposes analog Tanner graph decoding integrated with belief propagation, significantly boosting error correction performance.
• Extensive numerical simulations and open-source tools validate these methods, paving the way for scalable, fault-tolerant quantum computing.

Analog Information Decoding of Bosonic Quantum LDPC Codes

The paper "Analog information decoding of bosonic quantum LDPC codes" introduces novel methodologies for decoding bosonic quantum error-correcting codes within concatenated architectures with quantum low-density parity-check (QLDPC) codes. This work explores exploiting the analog syndrome information inherently available within bosonic qubit readouts, and presents versatile approaches applicable to any bosonic code incorporated into a concatenated quantum LDPC code architecture. Two major contributions of this paper include the introduction of quasi-single-shot protocols which dramatically reduce the necessity for repeated syndrome measurements, and the first-time implementation of time-domain decoding for QLDPC codes using the overlapping window method and an innovative analog single-shot decoding method.

Summary of Contributions

1. Analog Tanner Graph Decoding (ATD): This proposed decoding method leverages the continuous syndrome information from bosonic qubits in a way that enhances decoder performance significantly when compared to traditional methods. ATD allows seamless integration with existing belief propagation (BP) decoder frameworks and improves the decoding thresholds by utilizing all available analog data.
2. Single-shot Decoding Optimization: Single-shot decoding is critical due to the ease of mitigating syndrome errors without repeated syndrome measurements. The paper elaborates on analog Tanner graph decoding in single-shot scenarios and demonstrates improvements over classical single-shot decoding methods for the three-dimensional surface codes.
3. Quasi-Single-Shot Protocols: The authors propose a decoding protocol tailored for scenarios where full-fledged single-shot capabilities are absent. By integrating the analog information, the protocol drastically reduces the number of repeated syndrome measurements required for effective error correction, ensuring that it remains manageable even in codes that are not single-shot by nature.
4. Software Tools and Numerics: The research is underpinned by comprehensive numerical simulations, verified by open-source software implementations and made publicly available to support reproducibility and further exploration within the field.

Implications and Future Work

The implications of this research are wide-ranging. Practically, it offers a pathway toward reduced quantum computational overhead by decreasing resources required for maintaining fault tolerance. Theoretically, it bridges discrete variable and continuous variable quantum error correction, showing a path forward for leveraging the hardware efficiencies innate to bosonic systems.

Additionally, this work may pave the way for future studies investigating deeper integrations of analog information across multiple layers of error correction, spanning code types, dimensions, and computational environments. Future work will likely explore more complex circuit-level noise models, offering more realistic insights into large-scale quantum computational implementations, and seek optimization of BP decoders in the orchestration of analog data. There is also a promising research avenue in extrapolating these protocols to other quantum systems such as rotation symmetric bosonic codes and multi-mode GKP codes.

This paper makes significant steps toward refining quantum error correction protocols by aligning them more closely with the natural properties of the error-prone quantum systems they seek to stabilize, suggesting practical pathways toward scalable, fault-tolerant quantum computation.