Achieves 0.94 Fidelity: LiDMaS Advances Fault-Tolerant GKP Photonic Qubit Injection

Fault-tolerant quantum computation demands robust methods for creating high-fidelity logical magic states, even with the limitations of real-world quantum hardware. Researchers Dennis Delali Kwesi Wayo from the College of Computing, Georgia Institute of Technology, and colleagues demonstrate a novel architecture-level modelling framework , LiDMaS , to analyse magic-state injection in GKP photonic qubits. Their work, utilising a lightweight density-matrix simulator, bypasses complex wavefunction simulations and hardware specifics to efficiently explore architectural trade-offs for fault-tolerance. By systematically varying squeezing levels, loss probabilities, and surface-code distances, the team reveals crucial relationships between these parameters and logical fidelity, achieving success probabilities exceeding 94% and identifying minimum squeezing requirements for scalable quantum architectures , offering vital quantitative design guidance for future quantum computers.

The research team developed a repeat-until-success injection protocol, coupled with outer surface-code protection, to overcome limitations imposed by finite squeezing and photon loss, critical challenges in building scalable quantum computers. By mapping finite squeezing to effective logical dephasing, incorporating depolarizing noise, and treating loss as heralded erasure, we accurately model realistic error characteristics.

Density Matrix Simulation of Logical Qubit Errors reveals

Researchers represented encoded qubits with 2×2 density matrices, modelling logical operations via standard matrix algebra to enable computationally efficient exploration of architectural trade-offs while preserving essential error propagation characteristics. Finite squeezing was mapped to effective logical dephasing, while depolarizing noise and photon loss were incorporated at the logical level as heralded erasure processes, streamlining the simulation and focusing on key error mechanisms. The research team systematically varied squeezing values from 8 to 16 dB, baseline loss probabilities between 0.01 and 0.03, and surface-code distances d = 1, 3, 5, and 7 to comprehensively evaluate performance. Experiments employed a repeat-until-success (RUS) T-gate magic-state injection protocol, followed by outer surface-code protection, allowing the team to assess repeat-until-success probability, average injection overhead, and logical magic-state fidelity across a broad parameter space.
Success probabilities consistently exceeded 0.94, demonstrating robust performance, with an average injection overhead remaining close to unity, a significant achievement for practical quantum computation. After outer-code protection, logical fidelities reached approximately 0.77 to 0.80, exhibiting weak sensitivity to moderate loss but a strong dependence on squeezing levels. Scientists harnessed a composite noise map to model logical qubit behaviour, incorporating phase noise from finite GKP squeezing, depolarizing noise from imperfect Clifford operations, and photon-loss-induced erasure. Finite-energy GKP states’ residual phase uncertainty was modelled as a Pauli-Z channel, with an effective dephasing probability linked to the squeezing parameter via a monotonic proxy mapping, pZ(s) = min[0.5, αse−βs], capturing the expected improvement with increased squeezing.

Depolarizing noise, accounting for residual errors, was implemented using a depolarizing channel, while photon loss was treated as a heralded erasure process that terminates injection attempts without introducing unheralded logical errors. This layered abstraction, logical GKP encoding, RUS-based magic-state preparation, and outer-code suppression, provides a transparent and computationally efficient framework for evaluating fault-tolerant performance. The system delivers crucial insights into the dominant constraints on fault-tolerant photonic quantum computation, bridging the gap between decoder-centric analyses and system-level gate synthesis. These results underscore the central importance of squeezing improvements for enhancing logical gate quality, while highlighting the comparatively benign role of photon loss in heralded, RUS-based photonic architectures, a key finding for future development.

GKP Qubit Magic-State Preparation and Surface-Code Performance demonstrate

Scientists achieved success probabilities exceeding 0.94 across a range of parameters in a study of fault-tolerant quantum architectures. Researchers investigated logical T-gate magic-state preparation in GKP-encoded qubits, employing a repeat-until-success injection protocol combined with outer surface-code protection. Experiments systematically varied squeezing values from 8 to 16 dB, baseline loss probabilities from 0.01 to 0.03, and surface-code distances of 1, 3, 5, and 7 to comprehensively assess performance. Results demonstrate that the average injection overhead remained close to unity throughout the parameter sweeps.

Measurements confirm logical fidelities reached approximately 0.77 to 0.80 after outer-code protection, exhibiting weak sensitivity to moderate photon loss. However, a strong monotonic dependence on squeezing was observed, highlighting its critical role in maintaining fidelity. Sensitivity analysis revealed finite squeezing as the dominant continuous error source, while loss primarily impacted heralded failure rates rather than logical quality. Specifically, phase-boundary diagrams pinpoint the minimum squeezing needed to satisfy success-probability thresholds of ≥0.95 and logical-fidelity targets of ≥0.79 as a function of code distance.

These quantitative design guidelines are crucial for scalable, fault-tolerant photonic quantum architectures. The study’s framework represents logical qubits with 2×2 density matrices and models noise as effective logical channels, simplifying analysis without sacrificing physical relevance. Scientists mapped finite GKP squeezing to an effective Pauli-Z dephasing channel, while treating photon loss as a heralded erasure process that terminates unsuccessful attempts. This approach allowed for efficient exploration of a wide parameter space and direct correlation with experimentally measurable quantities. The research provides valuable quantitative data linking experimentally tunable parameters to operational metrics like success probability, overhead, and logical fidelity, addressing a critical gap in current understanding. This breakthrough delivers crucial insights for advancing photonic quantum computing and realizing scalable fault-tolerant systems.

Squeezing limits GKP magic state fidelity—a crucial resource

This research focused on preparing high-fidelity logical magic states, accounting for realistic constraints like finite squeezing and photon loss. The findings demonstrate that logical magic-state injection is robust against moderate photon loss, maintaining a near-unity average overhead across studied parameters. However, finite squeezing significantly limits logical fidelity, emerging as the dominant error source, a distinction highlighted by sensitivity and phase-boundary analyses. The authors acknowledge a limitation in not exploring extremely high loss regimes, and suggest future work could investigate the impact of more complex noise models.