Fusion-based qLDPC Codes with Quantum Emitters Achieve Low-Overhead, Fault-Tolerant Quantum Computation

Quantum error correction represents a critical challenge in realising practical quantum computers, and researchers continually seek codes that balance robust performance with efficient implementation. Susan X. Chen, Matthias C. Löbl, and colleagues at the University of Bristol and the Niels Bohr Institute now demonstrate a promising approach using quantum low-density parity-check (qLDPC) codes, which offer the potential for higher encoding rates than existing methods. The team proposes a novel implementation of these codes using a fusion-based architecture and resource states generated by quantum emitters, allowing for the deterministic correction of errors. This work achieves performance comparable to established topological codes, but with the significant advantage of increased data storage capacity, representing a substantial step towards scalable, fault-tolerant quantum computation.

These codes are particularly well-suited for fusion-based photonic implementations, as this platform readily supports non-local connections. Researchers propose a method to implement any Calderbank, Shor, Steane (CSS) qLDPC code with fusions and photonic resource states, which can be deterministically produced.

Photonic Fusions Implement qLDPC Codes

Scientists have developed a method to implement Calderbank-Shor-Steane (CSS) quantum low-density parity check (qLDPC) codes using photonic fusions and resource states, offering a pathway to fault-tolerant quantum computing with improved encoding rates. This work addresses limitations of topological codes, which, while robust, suffer from low encoding efficiency and substantial overhead when scaling to larger qubit numbers. The team engineered a system that leverages the inherent capabilities of photonic qubits to facilitate long-range interactions, crucial for implementing qLDPC codes on planar geometries. The core of this approach involves constructing logical memories solely through photonic fusions, probabilistic two-qubit operations, and deterministic resource states generated by quantum emitters.

Researchers designed a specific architecture for a [[72, 12, 6]] Bivariate Bicycle qLDPC code, and extended the method to be generalizable to any CSS qLDPC code. This construction relies on foliated cluster states, where each layer performs either X or Z-checks, and utilizes optical fibres to establish long-range connections between qubits. The experimental setup involves coupling data qubits to ancillary qubits at discrete time intervals to measure parity checks, and employs beamsplitters, phase shifters, and detectors to perform swap fusions. Scientists meticulously analysed the performance of these constructions under realistic noise conditions, including erasures due to fusion failure or photon loss, as well as Pauli errors. The results demonstrate that this fusion-based approach achieves comparable performance to topological architectures, despite the significantly higher encoding rate, representing a substantial advancement in the field of fault-tolerant quantum computing.

QLDPC Codes Match Topological Quantum Performance

Scientists have developed a method to construct quantum computing lattices using low-density parity check (qLDPC) codes, offering a pathway to more efficient encoding of quantum information with reduced overhead. This work focuses on fusion-based quantum computing, where resource states are linked via two-qubit fusion measurements to implement logical memory. The team demonstrated this approach using Bivariate Bicycle qLDPC codes, specifically the [[144, 12, 12]] code, achieving an error pseudo-threshold of 0. 2% and an erasure pseudo-threshold of 9%. Experiments revealed that the performance of these qLDPC constructions is comparable to that of topological architectures, despite the significantly higher encoding rate offered by qLDPC codes.

To improve tolerance to photon loss, a dominant source of noise in photonic platforms, researchers employed a repeat-until-success (RUS) scheme during fusion operations. Monte Carlo simulations, encompassing 105 trials, were performed on lattices built from Toric and Bivariate Bicycle qLDPC codes to evaluate photon loss thresholds. Results demonstrate that the [[144, 12, 12]] code lattice saturates at a photon loss pseudo-threshold of around 3% with a maximum of 8 repetitions in the RUS scheme. This 3. 4% threshold, achieved with the modified RUS procedure, surpasses previously reported loss thresholds for equivalent implementations of the Toric code. Although the Toric code exhibits a marginally higher threshold, the ability of the Bivariate Bicycle codes to encode a much larger number of qubits makes them highly attractive for future development. The team’s work provides a pathway to dramatically reduce resource overhead while maintaining competitive performance, paving the way for more efficient and scalable fault-tolerant photonic quantum computers.

QLDPC Codes Enable Lattice Error Correction

This research demonstrates a new method for constructing quantum error correction schemes using low-density parity check (qLDPC) codes, offering a potentially significant advantage over existing topological codes due to their higher encoding rates. The team successfully mapped these codes onto a lattice structure suitable for fusion-based quantum computing, a platform well-suited to implementing the necessary connections between qubits. This construction utilises resource states that can be reliably produced using current experimental techniques, particularly within photonic systems where qubit interactions can be achieved through optical fibres. The resulting error correction schemes achieve performance comparable to that of topological codes, despite encoding more quantum information with fewer resources. While the initial results indicate a slightly lower threshold for error correction compared to some topological codes, the substantial increase in the number of encoded qubits makes this approach highly promising. Future work will focus on incorporating more realistic noise models into simulations to guide the development of practical, fault-tolerant photonic quantum computers.